Question

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places

$2^x=101$

Short answer

The approximate value of x for the equation$2^x=101$is$6.658$

Step-by-step solution

Step 1. Given data 

The given Logarithmic Equation is$2^x=101$

Step 2. Use logarithms

Take logarithms to both sides of the equation

$$\begin{gathered} 2^x=101 \\ \log 2^x=\log 101 \end{gathered}$$

Step 3. Apply power property of logarithm

Use power property of logarithm

$$\begin{gathered} \log 2^x=\log 101 \\ x\log 2=\log 101 \end{gathered}$$

Step 4. Value of x

Solve the equation for x

$$\begin{gathered} x\log 2=\log 101 \\ x=\frac{\log 101}{\log 2} \\ x\approx 6.658 \end{gathered}$$