Posted by **Jessie** on Thursday, December 19, 2013 at 11:42pm.

1. Evaluate 4^(log base4 64) + 10^(log100)

2. Write 1+log(base2)x^3 as a single logarithm

3. Write log(base b)√(x^3 y z^6)

4. Solve log(base 2)x-log(base 2)6=log(base 2)5+2log(base 2)3

5. Solve 3^(2x) = 9(81^x)

6. Solve 3^(2x)=7^(3x-1). Round answer to two decimal places.

7. Solve log(x+3) + log(x-2) = log(3x+2)

- Advanced Functions/ Precalculus Log -
**Steve**, Friday, December 20, 2013 at 12:24am
By definition, b^{logbN} = N

#1. 64+100 = 164

#2. 1 = log2, so you have

log2+log(x^3) = log(2x^3)

#3. 1/2 (3logx + logy + 6logz)

#4. supressing the "base 2" for readability, we have

logx - log6 = log5+2log3

log(x/6) = log(5*3^2)

x/6 = 45

x = 270

Actually, since all the logs are the same base, the base doesn't really matter.

#5. Since 9=3^2 and 81=3^4, you have

3^(2x) = 3^2 * 3^4x

3^2x = 3^(2+4x)

2x = 2+4x

x = -1

Check: 3^-2 = 1/9

9(81^-1) = 9/81 = 1/9

#6.

3^(2x) = 7^(3x-1)

2x log3 = (3x-1) log7

2x/(3x-1) = log7/log3

x = 0.53

#7.

log (x+3)(x-2) = log (3x+2)

(x+3)(x-2) = (3x+2)

x = -2 or 4

- Advanced Functions/ Precalculus Log -
**Jessie**, Friday, December 20, 2013 at 2:55am
Thanks a lot!

- Logs - correction -
**Steve**, Friday, December 20, 2013 at 12:14pm
#7. Actually, x = -2 needs to be discarded, since log(x-2) is not defined there.

## Answer This Question

## Related Questions

- Algebra 2 - -Explain the difference between log base b (mn) and ( log base b of ...
- check! - here is the question: log5(x-4)= log7x solve for x. These are just base...
- math - write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of...
- precalc - Solve: round to the thousandths if necessary! 1) 4^3/4x+5 = 12 2) log(...
- math - Logarithm!!! Select all of the following that are true statements: (a) ...
- Precalc - 1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1) 2...
- Algebra - In the logarithmic expression . . . log(base 4) 8 , how does the base ...
- Trig - log base b 64 - log base b 16 = log base 4 16 solve for the variable.. i...
- math - Given that 2 log base2 (x+15) - log base2 x = 6 1.Show that x^2 -34x +225...
- math - Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x-9...

More Related Questions