Question

Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4^-x=2.6What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set { } (simplify your answer. type an exact answer)B. There is no solution

Answer 1

Given:

`4^(-x)=2.6`

To solve for x:

Taking log on both sides

`\begin{gathered} \log 4^(-x)=\log 2.6 \\ -x\log 4=\log 2.6 \\ -x=(\log 2.6)/(\log 4) \\ -x=0.689255811 \\ x=-0.689255811 \\ x\approx-0.689 \end{gathered}`

Hence, the value of x is -0.689 (rounded to three decimal places).