Math Homework Help Please: ?

Question

Can anyone help me solve this? Thanks.

log5^3x = log2^x+1

Note: the "^" means that the following is in super script

Ex. 4^1 = 4, 4^2 = 16.

Thanks!

Answer 1

Remember the rules of logs, specifically:

log a^b = b log a

So,

log 5^3x = log 2^x + 1

3x log 5 = x log 2 + 1

3x log 5 - x log 2 = 1

x(3 log 5 - log 2) = 1

And remember,

log(a/b) = log a - log b

so

x(log 5^3 - log 2) = 1

x log(125/2) = 1

x = 1/log(125/2)

Grab a calculator.