Question

Solve 4^x+2 = 12 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

The value of x is 1.66

Step-by-step explanation:

Let use revise the rules of exponential and logarithmic equations

1. If y = $b^{x}$, then $log_{b}(y)=x$

2. $log_{b}(y) = \frac{log(y)}{log(b)}$

Use the rules above to solve the problem

∵ $4^{x}+2=12$

- Subtract 2 from both sides

∴ $4^{x}=10$

change the exponential equation to logarithmic equation

∴ $log_{4}(10)=x$

∵ $log_{4}(10) = \frac{log(10)}{log(4)}$

∴ x = $\frac{log(10)}{log(4)}$

∴ x = 1.66

The value of x is 1.66

Learn more:

You can learn more about logarithmic function in brainly.com/question/10633485

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