# This log equation

## Homework Statement

2.3(1.2)^5z = 3(4.1)^z solve for z

## Homework Equations

the properties of logarithm

## The Attempt at a Solution

okay I first divided the 3 with 2.3 and got 1.304 then i brough the 5z and the z down which gives me 5z log(1.2)=1.304 z log(4.1) then i plugged log of 1.2 and 4.1 into the calculator and got .079 and .613 which makes the equation 5z(.079)=1.034z(.613) i then distributed and got .395z=.8z which doesnt give me an answer is the answer no solutions or did i do sumthing wrong?

Hint: log( A B^z ) = log(A) + log(B^z) = log(A) + z log(B)

...which doesn't give me an answer. Is the answer that there are no solutions or did I do something wrong?

Yes, there are no solutions to this equation. Unless you used z because you want complex solutions, in which case the properties of logarithms aren't the same.

Yes, there are no solutions to this equation.

There is most definitely a solution to this equation. Take giant_bog's advice in using that log expansion rule.

There is most definitely a solution to this equation. Take giant_bog's advice in using that log expansion rule.

You are correct. My mistake.