Question

Help! Logs :(

Answer 1

Express each of the following in terms of \[\log_{3}a \]

Answer 2

(i)\[\log_{2}(a^4) \]
(ii) \[\log_{3}(9a^2) \]

Answer 3

\[\log_{2} (a^4) = 4\log_{2}(a)\]

Answer 4

you can take exponents and move them out front of the log.

Answer 5

so you need change of base

so if you have \[\log_{a}(x)\]

and need to change it to \[\log_{b}\]

the change of base is

\[\log_{a}(x) = \frac{\log_{b}(x)}{\log_{b}(a)}\]

this is required for the 1st question...

the 2nd question needs to be rewritten as

\[\log_{3}(9a^2) = \log_{3}(3^2) + \log_{3}(x^2)\]

now simplify it