Question

I need help finding the inverse of f(x)=7^3x-5 with work shown.

Answer 1

your f(x)=7^3x-5 is ambiguous

did you mean it the way your typed it or
f(x)=7^(3x-5)

The way you typed it:

let y = 7^3x - 5
y + 5 = 7^(3x) , another ambiguity, the way you typed it, it would be
(7^3)(x)
I will go with my last interpretation.

y + 5 = 7^(3x)
step 1 is to interchange the x and y variables , so we get
x + 5 = 7^(3y)
step 2 is to solve this new equation for y, this requires logs

log(x+5) = log ( 7^(3x) )
log(x+5) = 3x(log7)
x = log(x+5)/(3log7) , x > 5

if you meant y = 7^(3x-5)
then we get x = 7^(3y-5), and now take logs of that etc.

Answer 2

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