What is the inverse of 3a^{5x-1}+1 ?

The inverse of 3a^{5x-1}+1 is (ln((a(x-1))/3))/(5ln(a))

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inverse of 3a^{5x-1}+1

inverse

3 a^{5 x - 1} + 1

\frac{ln ( \frac{a ( x - 1 )}{3} )}{5 ln ( a )}

Solution steps

y = 3 a^{5 x - 1} + 1

Replace

x

with

y

x = 3 a^{5 y - 1} + 1

Solve for

y, x = 3 a^{5 y - 1} + 1

\frac{ln ( \frac{a ( x - 1 )}{3} )}{5 ln ( a )}

\frac{3 x}{8 - 5 x}

y = \frac{1}{3} (x + 5) - 3

y = \frac{1}{x + 7}

f (x) = 3 - 5 x - 7

f (x) = 3 + 2 - x

What is the inverse of 3a^{5x-1}+1 ?
The inverse of 3a^{5x-1}+1 is (ln((a(x-1))/3))/(5ln(a))