Question

I will fan and medal!

Answer 1

If \[\log_{a}5 = x \] and \[\log_{a}7 = y \] then \[\log_{a} \sqrt{1.4}\] =

Answer 2

The hint:
\(\color{#000000 }{ \displaystyle 7/5=1.4 \quad \Longleftrightarrow \quad \sqrt{7/5}=\sqrt{1.4} }\)

And the rules are\( : \)

\(\color{#000000 }{ \displaystyle \log_a(b)+\log_a(c)=\log_a(b\cdot c) }\) (1) \({\tiny \\[0.8em]}\)
\(\color{#000000 }{ \displaystyle \log_a(b^c)=c\log_a(b) }\) (2)

Answer 3

I forgot to mention, another rule,

\(\color{#000000 }{ \displaystyle \log_a(b)-\log_a(c)=\log_a(b\div c) }\) (3)

Answer 4

Thank you :)
I get it now

Answer 5

Ok, so using the rule, you need to make some expression (and modify it as you go) that will get you to \(\log_a(\sqrt{1.4})\)