Question

Express as a single logarithm. Simplify, if possible. loga a/sqrtx - loga sqrtax
(The a's next to log are subscript, a/sqrtx is a fraction, sqrtx means square root of x and the same goes for sqrtax)

Answer 1

\[\large \log_a(\sqrt{x})-\log_a(\sqrt{ax})\]?

Answer 2

\[\large \log_a(\frac{a}{\sqrt{x}})-\log_a(\sqrt{ax})\] maybe?

Answer 3

yes

Answer 4

there are several ways to do this
one is to break apart right away, the other is to combine them as
\[\log_a(\frac{a}{\sqrt{x}\sqrt{ax}})\]

Answer 5

or
\[\log_a(\frac{a}{x\sqrt{a}})\]

Answer 6

then since \(\frac{a}{\sqrt{a}}=\sqrt{a}\) you have
\[\log_a(\frac{\sqrt{a}}{x})\]

Answer 7

or
\[\log_a(\sqrt{a})-\log_a(x)=\frac{1}{2}-\log_a(x)\]

Answer 8

thanks satellite, you are helping my daughter so much

Answer 9

yw