Question

write the expression as a single logarithm
(parentheses after log is log base)

4log(a) Y-1/3log(a) Z+5log(a) W

Answer 1

is the expression

1.

\[\frac{4\log_{a}(y) - 1}{3\log_{a}(z)+5\log_{a}(w)}\]

or

2. \[4\log_{a}(y) - \frac{1}{3} \log_{a}(z) + 5\log_{a}(w)\]

Answer 2

expression 2

Answer 3

ok...you need to know about powers and logs

\[\log(a^b) = b \times \log(a)\]

so you need to rewrite each log with a power

e.g.

\[4 \log(y) = \log(y^4)\]

the next one the power is 1/3 and the last log, the power is 5

Answer 4

next you need the laws for dividing and multiplying

multiplying

\[\log(ab) = \log(a) + \log(b)\]

dividing

\[\log(\frac{a}{b}) = \log(a) - \log(b)\]

Answer 5

what I came up with is \[\log_{a} \frac{ y ^{4}w ^{5} }{ \sqrt[3]{z}}\]

is this correct? am I missing the base of the log?

Answer 6

yep... that looks really good...

well done the only thing, to avoid confusion it should be in brackets

\[\log_{a} (...)\]

Answer 7

brackets or parentheses?

Answer 8

is there another way to write cube root at the bottom of a fraction?

Answer 9

brackets or parentheses.... doesn't matter... I'd use brackets... the only alternative for the denominator is index form..

Answer 10

could I write \[Z ^{\frac{1 }{ 3}}\]

Answer 11

yep... thats fine... but for me... using the cube root... is neater..

Answer 12

cool yeah I agree, but the online form im using doesnt have the option of writing it that way

Answer 13

thanks for your help!

Answer 14

good luck