Solve the equation. Round to the nearest hundredth. Show work. 4^(-5x-7) = 6^(2x-1)

Question

Solve the equation. Round to the nearest hundredth. Show work.


`4^(-5x-7) = 6^(2x-1)`

Answer 1

`x=-0.75`

Explanation:

The given equation is

`4^(-5x-7)=6^(2x-1)`

We take logarithm of both sides to base 10.

`\log(4^(-5x-7))=\log(6^(2x-1))`

`(-5x-7)\log(4)=(2x-1)\log(6)`

We expand the brackets to get;

`-5x\log(4)-7\log(4)=2x\log(6)-\log(6)`

Group similar terms;

`-7\log(4)+\log(6)=2x\log(6)+5x\log(4)`

`-7\log(4)+\log(6)=(2\log(6)+5\log(4))x`

`(-7\log(4)+\log(6))/((2\log(6)+5\log(4)))=x`

`x=-0.752478`

To the nearest hundredth.

`x=-0.75`