Question

ln5x+ln3x=9

Answer 1

is that
\[\ln5x+\ln3x=9\qquad\text{ or }\qquad\ln_5x+\ln_3x=9\]

Answer 2

the first one

Answer 3

when the logarithms have the same base
\[\ln x+\ln y=\ln(xy)\]

Answer 4

so does it look like this ln5x+ln3x=ln15

Answer 5

the right side is just a 9...

Answer 6

so you have this:
ln(15x^2)=9

Answer 7

you need to write this out in exponential form:
e^9 = 15x^2

Answer 8

now solve for x...

Answer 9

ln5x+ln3x=9
ln((5x)(3x))=9
ln(15x^2)=9
e^(ln(15x^2)=e^9
15x^2=e^9
x^2=e^9 /15
\[x=\pm \sqrt{\frac{e^9}{15}}\]