Question

How do you solve `7.74^(x + 3) = 10.2`?

Answer 1

I found: `x-1.8651`

Explanation:

You can first take the natural log of both sides:

`ln(7.74)^(x+3)=ln(10.2)`

Then you can use the property of logs that tells us that:

`logx^b=blogx`

and write:

`(x+3)ln(7.74)=ln(10.2)`
rearrange:

`x+3=(ln(10.2))/ln(7.74)`
`x=(ln(10.2))/ln(7.74)-3`
`x=1.1348-3=-1.8651`