Problem 24 - College Algebra Essentials

Question

Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$10^{x}=8.07$$

Step-by-Step Solution

Answer

After evaluating the common logarithm, the solution for x would be approximately 0.91.

Step 1: Transform the equation by applying log

Apply the logarithm transformation to both sides of the equation in order to allow for the exponent to be solved. This can be done by taking the common (base 10) logarithm of both sides, which gives \(\log_{10}(10^{x})=\log_{10}(8.07)\).

Step 2: Simplify the equation

The logarithm can simplify the equation to the exponents, yielding the equation \(x=\log_{10}(8.07)\).

Step 3: Calculate the value of x

Finally, use a calculator to evaluate \(\log_{10}(8.07)\). This gives a decimal approximation for x, rounding to two decimal places.