MATH SOLVE

2 months ago

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

Accepted Solution

A:

The value of x is 1.66Step-by-step explanation:Let use revise the rules of exponential and logarithmic equations1. If y = [tex]b^{x}[/tex], then [tex]log_{b}(y)=x[/tex]2. [tex]log_{b}(y) = \frac{log(y)}{log(b)}[/tex]Use the rules above to solve the problem∵ [tex]4^{x}+2=12[/tex]- Subtract 2 from both sides∴ [tex]4^{x}=10[/tex]change the exponential equation to logarithmic equation∴ [tex]log_{4}(10)=x[/tex]∵ [tex]log_{4}(10) = \frac{log(10)}{log(4)}[/tex]∴ x = [tex]\frac{log(10)}{log(4)}[/tex]∴ x = 1.66The value of x is 1.66Learn more:You can learn more about logarithmic function in brainly.com/question/10633485#LearnwithBrainly