Question

Y=8^x-13find the inverse for this function

Answer 1

Answer:
`f^(-1)(x)\text{ = }(\ln(x+13))/(\ln8)`Explanations:

The given function is:

`y=8^x-13`

Make x the subject of the formula:

`\begin{gathered} 8^x\text{ = y + 13} \\ \text{Take the natural logarithm of both sides} \\ \ln 8^x\text{ = ln (y + 13)} \\ x\ln \text{ 8 = }\ln (y+13) \\ x\text{ = }(\ln (y+13))/(\ln 8) \end{gathered}`
`\begin{gathered} \text{Let x be replaced by f}^(-1)(x)\text{ and y be replaced by x} \\ f^(-1)(x)\text{ = }(\ln (x+13))/(\ln 8) \end{gathered}`