Question

PLEASE HELP ASAP 25 PTS TO RIGHT/BEST ANSWER

Answer 1

Subtract 1111 from both sides

5{e}^{{4}^{x}}=22-115e​4​x​​​​=22−11


 

Simplify 22-1122−11 to 1111

5{e}^{{4}^{x}}=115e​4​x​​​​=11



 

Divide both sides by 55

{e}^{{4}^{x}}=\frac{11}{5}e​4​x​​​​=​5​​11​​



 

Use Definition of Natural Logarithm: {e}^{y}=xe​y​​=x if and only if \ln{x}=ylnx=y

{4}^{x}=\ln{\frac{11}{5}}4​x​​=ln​5​​11​​



 

: {b}^{a}=xb​a​​=x if and only if log_b(x)=alog​b​​(x)=a

x=\log_{4}{\ln{\frac{11}{5}}}x=log​4​​ln​5​​11​​



 

Use Change of Base Rule: \log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}log​b​​x=​log​a​​b​​log​a​​x​​

x=\frac{\log{\ln{\frac{11}{5}}}}{\log{4}}x=​log4​​logln​5​​11​​​​



 

Use Power Rule: \log_{b}{{x}^{c}}=c\log_{b}{x}log​b​​x​c​​=clog​b​​x
\log{4}log4 -> \log{{2}^{2}}log2​2​​ -> 2\log{2}2log2

x=\frac{\log{\ln{\frac{11}{5}}}}{2\log{2}}x=​2log2​


Answer= −0.171