Question

Please help:

Answer 1

To solve this problem we are going to use the power rule of logarithms: $ln(a^{x} )=xln(a)$. Or in words: the logarithm of a power is the power times the logarithm of the base. 
So, the first thing we are going to do is take natural logarithm, $ln$, to both sides of our equation:
$ln(5^{x+2} )=ln(9^{2x+3} )$
Now, by the power rule of logarithms:
$(x+2)ln(5)=(2x+3)ln(9)$
$\frac{(x+2)ln(5)}{2x+3} =ln(9)$
$\frac{x+2}{2x+3}= \frac{ln(9)}{ln(5)}$
$\frac{x+2}{2x+3} =1.365$
$x+2=1.365(2x+3)$
$x+2=2.73x+4.095$
$-1.73x=2.095$
$x=- \frac{2.095}{1.73}$
$x=-1.211$

Using our calculator we can conclude that $x$ is approximately -1.211 <span />