Question

Solve the following exponential equation. Round your answer to three decimal places.10ˣ = 9 x =

Answer 1

To solve the equation 10ˣ = 9, we find the logarithm of both sides of the equation.

`\begin{gathered} 10^x=9 \\ \text{ taking the log of both sides, we have} \\ \log 10^x=\log 9 \end{gathered}`

Using logarithm rule, we have

`\begin{gathered} x\log 10=\log 9 \\ \log 10=1 \\ \text{ Hence} \\ x=\log 9 \end{gathered}`
`x=\log 9=0.954`

/

x = 0.954