Question

How do you solve `17^ { 4m + 6} + 8= 60`?

Answer 1

`m = -1.151`

Explanation:

We're asked to solve for `m` in the equation

`17^(4m+6) + 8 = 60`

Subtract `8` from both sides:

`17^(4m+6) = 52`

This can be expressed in logarithmic form as

`log_17(52) = 4m+6`

According to the change-of-base formula:

`log_17(52) = (log52)/(log17) ~~ ul(1.3946`

Therefore,

`1.3946 = 4m + 6`

Subtract `6` from both sides:

`-4.605 = 4m`

Divide both sides by `4`:

`color(blue)(ulbar(|stackrel(" ")(" "m = -1.151" ")|)`

`---------------------`

We can check this answer by plugging it back in to the original equation:

`17^(4(-1.151)+6) + 8 = 60`

`17^(4(-1.151)+6) ~~ ul(52.2`

`52.2 + 8 ~~ 60`