Question

How do you solve `7^(x – 2) = 12x`?

Answer 1

A step in the correct direction!! Perhaps someone else can take it further. I used the Iteration method.

Explanation:

`color(red)("Method 1")`
Plot the straight line graph of `12x`
Plot the curve of `7^(x-2)`
The intersections are where the values for `x` are.

Or try iteration for `x =7^x/588`

`color(red)("Method 2")`
`7^(x-2) -> (7^x)/(7^2)`

so `7^(x-2) = 12x -> 7^x = (7^2)(12)x`

`7^x = 588x`

Taking logs
`x ln(7) = ln(588) + ln(x)`

`x = (ln(588) + ln(x))/(ln(7))`

By iteration

Set seed value as 1
`x ~= 3.988` to 3 decimal places

I could not find the seed for the lower one which is in the region of
`x ~= 0.0016` to 5 dp

Graphs of the log method: