Question

express as a single logarithm:

3logb(3(sqrt(x))-2logb(x)

Answer 1

\[3\log(3\sqrt3)-2\log(x)\] like that ?

Answer 2

no that is not right, how about
\[3\log(3\sqrt{x})-2\log(x)\]

Answer 3

start by turning the coefficients in to exponents and write
\[\log((3\sqrt{x})^3)-\log(x^2)\]

Answer 4

then the subtraction becomes a division, and you get
\[\log\left(\frac{27(\sqrt{x})^3}{x^2}\right)\]

Answer 5

this part \(\frac{27(\sqrt{x})^3}{x^2}\) needs some cleaning up, but that is the idea