Questions on Algebra: Logarithm answered by real tutors!

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Question 865839: - + = 2
Please solve for x
Please show all steps
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Question 734457: log10x-log(x-3)=log2
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Question 883161: log2(x - 6) + log2(x - 4) = log2 x solve the logarithmic equation. and round.
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Question 954792: Solve log2(x-2)-log2(x+5)=3
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Question 22137: log2x+log2(x-6)=4
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Question 735204: Please show how to solve:
Log base10(n^2 � 90n) = 3
Thank you
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Question 1111913: Rachel Spender wants to invest $4000 in savings certificates which bear an interest rate of 7.25% compounded semi-anually. How long a time period should she choose in order to save an amount of $4700?
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Question 1112016: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit.
a). If the temperature of the turkey is 141 Fahrenheit after half an hour, what is its temperature after 45 minutes?
b). When will the turkey cool to 100 Fahrenheit?
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Question 1130119: Could someone please assist with the question:
A pot of boiling soup with an internal temperature of 100� Fahrenheit was taken off the stove to cool in a 69�F room. After fifteen minutes, the internal temperature of the soup was 93�F.
To the nearest minute, how long will it take the soup to cool to 81�F?
Here is my work:
69+(100-69) * e= 69+31*e
93=69+31*e(-k*15)
31*e^(-k *15)= 93-69= 24
e^-15k= 24/31= .7742
-15K= ln(.7742)
k= -ln(0.7742)/ 15=0.017
T(t)= 69+31*e (0.017)=81
e(-0.017*t)= 81-69/31=.387
-0.017*t= ln(.387)
t= - ln (.387)/ (0.017)= 55.8 min

Click here to see answer by ikleyn(53742)

Question 1163697: unsolved 2020-08-22 10:07:30 It is believed that two quantities, z and d are Connected by the relationship of the form z=kd^n where k and n are provided that d doesn't exceed some fixed (but unknown)values D.An experiment produced the following data
D 750 810 870 930 990 1050 1110 1170
Z 2.1 2.6 3.2 4.0 4.8 5.6 5.9 6.1
a)Plot the values of log10Z against log10 d.Use these points to suggest a
value for D.
b)It is known tht for d < D,n is a whole number.Use your graph to find the value of n.Show also that k=5×10^-9
c) Use your value of n and the estimate k=5×10^-9 to find the value of d for which z=3.0.
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Question 166689: log3(x-2)+log3(x+4)=3
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Question 945331:
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Question 1088632: log3 (2x-1) = 2 x =
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Question 1026110: simplify the expression
log3 (x+1) -log3 (3x^2-3x-6)+log3 (x-2)
The 3 on each log is lowered
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Question 747802: log3(x+6)+log3(x-6)-log3x=2
solve the logarithmic equation
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Question 815452: if x*x+y*y=7xy, prove
log(x+y)=1/2(logx+logy)+log3
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Question 815452: if x*x+y*y=7xy, prove
log(x+y)=1/2(logx+logy)+log3
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Question 769077: if logx =4 and logy =3 Evaluate log square root of x divided by y squared
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Question 769077: if logx =4 and logy =3 Evaluate log square root of x divided by y squared
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Question 717220: log(base x)(1/4) = (-2/3)
log(
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Question 717220: log(base x)(1/4) = (-2/3)
log(
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Question 250018: solve:

Unfortunately I do not know how to put this without all the words. But this is a problem on one of my take home tests. I dont understand how to solve because I get for the log in the parentheses but now I don't knwo what to do?
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Question 1129970: Find the exact value of e^LOGe^2 16
The answer is 4, but I am unsure as to why.
If possible, please show multiple methods (with step by step breakdown). Here is what I've gathered so far:
Method 1:
1. e^LOGe^2 2^4
2. e^(4/2)LOGe 2 ( I don't understand where the 4 divided by 2 comes into play, and which property dictates it )
3. e^2LOGe 2
4. e^LOGe 4 (Where did the 4 come from? Did both of the 2's get multiplied?)
5. =4
Method 2:
1. e^LOGe^2 16
2. e^(1/2)LN 16 (Where did the 1/2 come from?)
3. sqrt(e^LN 16) (Why is the entire expression inside the square root?)
4. sqrt(16) (Why did the "e^LN" portion inside the square root disappear?)
5. =4
Is it also possible to solve this problem by using the base change method?
Thanks in advance.
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Question 130716: I have tried to figure this equation but it doesn't come out with the right answer. Please can you help me?
9^x = 1/3sqrt 3
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Question 71721: log base 2 x ^(log base 2 x) =4
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Question 71721: log base 2 x ^(log base 2 x) =4
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Question 492608: I need help with these questions
5^x=125
8^x+1=16^x
81^(3/4)=x
8^(-2/3)=x
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Question 80251: log 4x= log 5+log(x+1)
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Question 617405: if log base b (2)=x and log base b (3)=y, evaluate the following terms of x and y:
log base b (24)=
log base b (216)=
log base b (16/27)=
(log base b (27))/(log base b (4))=
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Question 895678: log base 2 (log base 3 (log base 5 of x)) = 0
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Question 5994: This equation is giving me issues.
log(base2)(x-6)+log(base2)(x-4)-log(base2)x = 2
Solve for x. Reject any value of x that produces the logarithm of a negative number or 0.
What I've done:
log(base2)(x-6)(x-4)-log(base2)x = 2
log(base2)(x-6)(x-4)/x = 2
(x-6)(x-4)/x = 2^2 = 4
4 = (x-6)(x-4)/x
There is where I am stuck.
Some help on this would be great. Thanks.
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Question 492607: I need help with these questions
5^x=125
8^x+1=16^x
81^(3/4)=x
8^(-2/3)=x
log(base2)32=x
log(base x) (1/9)=-2
log(base4)x=3
Log(base3)(x+7)=Log(base3)(2x-1)
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Question 174799: log(base2)log(base3)log(base4)2^n=2
I don't understand how to solve this.
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Question 1076081: solve log base 5(x+2) + log base 8(x+4) = log abse 8(2) + log base 8(4)
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Question 206454: 2 log(base 4) 9 - log(base 2) 3
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Question 206454: 2 log(base 4) 9 - log(base 2) 3
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Question 416851: log base 2 (x-2)+log base 2(8-x)-log base 2(x-5)=3
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Question 840261: log (base 3) of x minus log (base 3) of (x-5) = log (base 3) of A
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Question 414908: solve log(base a)x= 2log (base a)3+ log(base a)5
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Question 744476: 1. Show that log(base 1/c)x = log(base c)1/x
Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)
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Question 244998: given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm.
log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^6 times x^2)
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Question 315262: evaluate the logarithm.
1. log (base 7) 1/49
write the expression as a single logarithm
2. 5log (base b)q+3 log(base b)w
3. 4 log x-6 log (x+2)
4. solve 4^2x=111
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