Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Question 428709: Please help! I would really appreciate it!
>Solve the equation (1/3)log7 64+ (1/2)log7 121= log7 x
>Find log3 25 given that log3 5= 1.465
>If log.5=-.3010, what is the mantissa of log.5?
Please include steps for each! Thanks again
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Question 428913: simplify each number (-8)2/3

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Question 428913: simplify each number (-8)2/3

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Question 428917: -27^-4/3
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Question 428880: Let f(x)=3x-3 and g(x)=x^2-4x+3. Find the following
2f(x)
Click here to see answer by richard1234(7193)

Question 429093: Solve 2(5^(x-2))= 9 -5^(x-2). (Hint: First solve for 5^(x-2) Then take the log (or ln) of both sides.) Please help. I do not understand this. Thanks in advance.
Click here to see answer by richard1234(7193)

Question 429092: Solve the equation 3^(4x+2) =9^(x-1) (Hint: Write both sides as a power of 3 and then match the powers.)
I do not get this problem even with the hint. Please help. :) Thanks!
Click here to see answer by richard1234(7193)

Question 429205: f(x)=x2-1;g(x)= 1
----
x+1
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Question 429543: how do you write an exponential function y=ab raised to the x with the points (0,1), (2,4)
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Question 429548: Calculate the quotient and the remainder
12x^4-x^3+4x^2+6x-7 / 3x^2+2x
Click here to see answer by Gogonati(855)

Question 429482: log3(y-2)+log3y=4
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Question 429696: What is the log base 2 of 8? (log5,8)
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Question 429883: Evaluate log4 64
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Question 430364: how do I find the decimal of three places. I have the problem (x+5)^2=4. I cant figure out the three decimal thing. Coukld someone please help me
Click here to see answer by Alan3354(69443)

Question 430363: Ok I have a problem that I believe I solved but I just want to be sure I am completing it correct. So here is the problem
Zero coupon bonds do not yield periodic interest. Instead the purchaser buys the bond for less then the face value and then is paid full face value when the bond is mature. Before the bond is matures, its market value(price paid by a purchaser in the bond market) is determined by the prevailing market interest rate.
Below consider a 15 year bond with a face value of $1000
A) Determine the current market value of the bond if the prevailing market interest rate is 5% per year.
B) Determine the prevailing market interest rate if the correct market value of the bond is $300

So this is how I approached part A
Current value = 1000
Initial value = X
Rate 5%
Time = 15 years
term = 1
So 1000=x(1+(0.05/1))^15
Which comes out to $481.01
Is this correct? Buying a bond for approx. half value seems logical.

For Part B I approached it the following way.
Current value=1000
Initial value=300
rate = x
time = 15 years

1000=300e^r(15)
solved for r getting 8.02% This seems logical as a higher rate would mean a lower initial value
I am new to these problems so just want to be sure I am approaching them correctly. Thank you in advance for your help.

Click here to see answer by stanbon(75887)

Question 430407: Give exact and approximate solution to three decimal places. (x+5)^2=4. I don't under stand the three decimal places

Click here to see answer by sudhanshu_kmr(1152)

Question 430485: Determine the nature of the solutions of the equation.
y^2=1/8y+3/5
Click here to see answer by stanbon(75887)

Question 430776: Use the change of base formula to calculate log3 21
Click here to see answer by vleith(2983)

Question 431001: Height of trees:
The height (in feet) of a certain kind of tree is approximated by
h(t)= 160/1+240e^-0.2t. Where t is the age of the tree in years. Estimate the age of an 80-ft tree.

Click here to see answer by solver91311(24713)

Question 431004: Lengths of fish:
The length (in centimeters) of a typical Pacific halibut t year old is approximately f(t)=200(1-0.956e^-0.18t). Suppose a Pacific halibut caught by Mike measures 140cm. What is its approximate age?
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Question 431104: What is [g * f](x) if f(x)= x^2 + 1 and g(x)= -2x+1
Click here to see answer by Gogonati(855)

Question 431338: Simplify the logarithm
log9 27
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Question 431338: Simplify the logarithm
log9 27
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Question 431345: Simplify the logarithm
log1/3 3 root 81
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Question 431342: Simplify the logarithm
log2 4 root 2
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Question 431884: Given log9 = 0.95 and log2 = 0.30, find the following using the logarithm properties
log81
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Question 432025: What is t to the negative 4 power
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Question 432033: Help me solve ln 12+ ln x = ln (12+x) where did I go wrong. I know that this is incorrect.
Click here to see answer by ewatrrr(24785)

Question 432120: I do not understand how to solve f(x)=ca^x. can someone show me step by step examples of how to solve.
Click here to see answer by richard1234(7193)

Question 432333: I need to convert the following to decimal notation.
8.07*10^7
Thank you
Click here to see answer by stanbon(75887)

Question 432396: Solve the equation. (Hint: the bases cannot be made the same.)
8+10^x=908
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Question 432395: Solve the equation. (Hint: the bases cannot be made the same.)
3^x=20
Click here to see answer by pheonix1974(2)

Question 432469: Change from exponential form to logarithmic form and solve for x:
3^x-2=7
A)solve for x (exact solution)
B)use calculator to solve for x and round to nearest thousandth
Am I doing this right?
A) log3 of 3^x-2=log3 of 7
x-2=log3 of 7 (+2 to both sides)
x=(log3 of 7)+2
x=(ln7/ln3)+2
Would this be my final answer for A?
B) Same steps as above
x=(ln7/ln3) +2
x=3.771 approximately rounded to the nearest thousandth
I just need to know if I am doing this correctly, and getting the correct solutions. If not I have to figure out where I am going wrong. Please guide me.
Click here to see answer by MathLover1(20850)

Question 432553: One more for verification purposes:
IF something increases by 40% every 6 months what is the 1-year % increase?
Let S= something
S=(1+.40)^12 = S(1.40)^12 = S(56.59) = S increased by 56.59% in 1 year.

Correct?
Click here to see answer by ewatrrr(24785)

Question 432584: How do u solve this?
Log(Xsquared)=(logX)squared
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Question 432584: How do u solve this?
Log(Xsquared)=(logX)squared
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Question 432875: i really don't understand thisss.
2 log3 (x) + log 3 (5) = log3 (14x+3)

Click here to see answer by Alan3354(69443)

Question 432973: 80/(1+15e^-.06x)=50 ;

Click here to see answer by robertb(5830)

Question 433147: rewriting an expression with division of logs as a single log:
simplify log64/log6
Click here to see answer by katealdridge(100)

Question 433236: Need help with solving, If f(x)=2x+4, and g(x)=(x^2+x+5), find g(f(x))
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Question 433268: log3(x-2) = 1+log3(x-4) The logs have a base of 3. How do I solve this?
Click here to see answer by scott8148(6628)

Question 433334: how would you condense 8lnx-(2ln3+7lny)
Click here to see answer by stanbon(75887)

Question 433527: Use the "change of base" formula to find: log7 21
Click here to see answer by belle3833(46)

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