Question

14^x+1=36
Round to the nearest ten thousandth

Answer 1

\[\large 14^x+1=36\\
\large 14^x=36-1\\
\large 14^x=35\\
\large \log(14^x)=\log 35\\
\large x \log14 = \log 35\\
\large x = \frac{\log35}{\log 14}\approx 1.3472\]

Answer 2

actually maybe you meant instead \( \large 14^{x+1}=36\) ?

\[ \large 14^{x+1}=36\\
\large \log(14^{x+1})=\log 36\\
\large (x+1)\log 14 = \log 36\\
\large x \log14 + \log 14 = \log 36\\
\large x\log 14 = \log 36 - \log 14\\
\large x = \frac{\log 36 - \log 14}{\log 14}\approx 0.3579\]