Questions on Algebra: Logarithm answered by real tutors!

Tutors Answer Your Questions about logarithm (FREE)

Question 815452: if x*x+y*y=7xy, prove
log(x+y)=1/2(logx+logy)+log3
Click here to see answer by greenestamps(13292)

Question 815452: if x*x+y*y=7xy, prove
log(x+y)=1/2(logx+logy)+log3
Click here to see answer by MathTherapy(10699)

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.
Click here to see answer by MathTherapy(10699)

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)
Click here to see answer by n2(36)

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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Question 905391: log(6x-3)base 3=1+log(x-3)base3)
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Question 871834: Hi and thanks for the help! I was wondering how to solve log base square root 3 to the 1/9=x. also one other question is to change the exponential equation to a log... x^3=729
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Question 891810: log (base 3) x + log (base 5) 4x = 2
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Question 933453: Log(base 2) (x+14)+log(base 2)x=5
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Question 975452: 0= log base 5 (x-2) - log base 5 (2x)
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Question 698509: How do I solve the following logarithm for x?
The base of the log is x.
log64=3/2
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Question 22964: HELP =) !
resolving the Question 2570 (p200 - 250) : log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the base square root of 3
a tutor found x = 3^(1/4) or x = 1/3
I only found one answer x = 3^(1/4)
Who is right ? And where is the (my?) flaw ?
Thanks a lot !!!
Here is my answer :
logV""x(9) - logx(3) = 9 + 6logV""3(x)
(logx 9) / (logx V""x) - logx 3 = 9 + 6( (logx x) / (logx V""3) )
(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6( 1 / ( (logx 3) / 2 ) )
(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6 / ( (logx 3) / 2 )
2logx 9 - logx 3 = 9 + 6 ( 2 / logx 3 )
2logx 9 - logx 3 = 9 + 12 / logx 3
logx 3 ( 2logx 9 - logx 3 - 9 ) = 12
logx 3 ( 4logx 3 - logx 3 - 9 ) = 12
logx 3 ( 3logx 3 - 9 ) = 12
3(logx 3)^2 - 9logx 3 = 12
(logx 3)^2 - 3logx 3 = 4
logx 3 - 3 = 4 / (logx 3)
logx 3 - 3 = 1/4 logx 3
logx 3 - 3 = logx 3^(1/4)
logx 3 - logx 3^(1/4) = 3
logx (3/3^(1/4) ) = 3
x^3 = 3/3^(1/4)
x^3 = 3^(3/4)
x^3 = 3^( (1/4) * 3 )
x^3 = ( 3^(1/4) )^3
x = 3^(1/4)
Click here to see answer by MathTherapy(10699)

Question 34026: i am having a hard time answering these problems.
1. x=8log(100,10)
2. logx (1/16)=-2
3. log(x)=square root log(x)
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Question 673683: log(x+12)=2
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Question 79779: log(Base3)(x-1) -Log(base3)(x+2)=2
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Question 315119: if log(base3)x=7, evaluate the following. log(base3)9x

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Question 1204575: If log(3,x) = 8, evaluate the following.
log(3,9x)

I was given the answer 10 but I don't know the reasoning.
Click here to see answer by ikleyn(53560)

Question 921936: log (base 7) 2 + log (base 49) x = log (base 1/7) sqrt 3
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Question 1082504: Hi!! What is log base 4 of X - log base 16 of (x+3) = 1/2
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Question 29308: Condense the expression:
1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y
Please help me solve this. Thank You for your time.
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Question 153463: How do you Combine logs?
Log(base5)(x^2-1)-Log(base5)(x-1)
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