Question

Solve the following a) give the solution in calculator ready form( the exact value of x) and then b) approximate the solution to the nearest hundredth 7. 6^x-3 =52

Answer 1

`x=5.21`

Explanation:

By applying the law of exponents:

`\begin{gathered} 6^{\mleft\{x-3\mright\}}=52 \\ (x-3)\ln 6=\ln 52,\text{ Solve for x.} \\ x-3=(\ln 52)/(\ln 6) \\ x=(\ln52)/(\ln6)+3 \end{gathered}`

Round to the nearest hundredth:

`x=5.21`