# math

posted by .

logarithms?

log (base 9) x+3 log (base 3) x=14

• math -

log9(x) = log3(x) * log9(3)
what is log9(3)
9^log9(3) = 3
9^.5 = 3
so
log 9(x) = .5 log3(x)
Now the problem
.5 log3(x) + 3 log3(x) = 14
log3 (x^.5) + log3(x^3) = 14
log 3 (x^3.5) = 14
x^3.5 = 3^14
now use plain old base ten logs
3.5 log x = 14 log 3
log x = 1.91
x = 10^1.91 = 81.3
Check my arithmetic!!!

• math -

deeeeeeeeez ntus

## Similar Questions

1. ### Precalculus

I'm studying for my precalc exam and have completed 42 practice problems. I have 3 I need to answer that I can't. Please help. What is the base of the function G(x) = log subscript b x if it's graph has points (16,4)?
2. ### Math: Algebra2 Logarithms

Can someone help me find the value of B in this expression?
3. ### Logarithms

CONDENSE INTO THE LOG OF A SINGLE QUANTITY: (1) Base 7 2/3 log( z - 2 ) (2) 2 ln8 + 5 ln( z - 4 ) (3) Base 4 1/2 [ log( x + 1 ) + 2 log( x - 1 ) ] + 6 logx

1) use the properties of logarithms to simplify the logarithmic expression. log base 10 (9/300) log - log 300 log 9 = 2 log 3 log 300 = log 3 + log 100 = log 3+2 I just do not know how to put these together now!
5. ### Precalc

1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1) 2. 2^x+8 times 2^=x all over 2 = 3 3. if log base a of 3= x and log base a of 2 = y, find each of thefollowing in terms of x and y log base a (18a^3) thanks!!
6. ### math

Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x-9)) in a form with no logarithm of a product, quotient or power. After rewriting we will have: log(base 2)A+log(base 2)x+log(base 2)f(x) What is A and what is f(x)?
7. ### Algebra 2

-Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent?
8. ### Advanced Functions/ Precalculus Log

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). …
9. ### Logarithms

Prove that log base a of x divided by log base a/b of x is equal to 1+log base a of(1/b) Where do I start?
10. ### Econ math/logarithms

If log with base b (2)=0.39 and log with base b (3)=0.61 evaluate the following. log with base b (8). Simplify your answer. How to start?

More Similar Questions