Answer
$y\approx 0.2720$
Work Step by Step
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=25, y=2x+1, x=144$), we get:
$\log_{25}{144}=2x+1$
Next, recall the change of base formula (pg. 464):
$\log_{b}{m}=\dfrac{\log_{c}{m}}{\log_{c}{b}}$
Applying this formula to our last equation, we get:
$\log_{25}{144}=2x+1$
$\dfrac{\log_{10}{144}}{\log_{10}{25}}=2x+1$
$\dfrac{\log_{10}{144}}{\log_{10}{25}}-1=2x$
$\dfrac{1}{2}\frac{\log_{10}{144}}{\log_{10}{25}}-\frac{1}{2}=x$
$y\approx 0.2720$
We confirm that the answer works:
$25^{2\cdot0.2720+1}=144$
$25^{1.544}=144$
$144=144$
