Question

If logx^2-log2a=log3a, then logx expressed in terms of loga is equivalent to
i know the answer is (1/2)log6+loga but i don't get how

Answer 1

in this case do you know what is the index of logarithm when you write

logx^2 for example ?

Answer 2

yeah 1/2logx

Answer 3

i tought it log_2 x so for example so this in case when you dont wrote there what number is in place of 2

Answer 4

i don't know what u mean

Answer 5

try this http://www.rapidtables.com/math/algebra/Logarithm.htm

Answer 6

yeah i am just confused about what you're asking

Answer 7

moment

logx^2 -log2a = log3a add to both sides log2a what will get ?

Answer 8

logx^2 =log3a +log2a yes ?

Answer 9

yeah

Answer 10

logx^2 = 2logx bc. you know the formula log(a)^2 = 2log(a) yes ?

Answer 11

yeah

Answer 12

and so hope you know again that

log a -log b = log (a/b)

Answer 13

do you can using in this above case ?

Answer 14

sorry there are log a +log b = log(a*b)

Answer 15

\[\log(x^2)-\log(2a)=\log(3a) \]\[2\log(x)=\log(2a)+\log(3a)\]
\[2\log(x)=\log(6a^2)\]
\[2log(x)=\log(6)+\log(a^2)\]
\[2\log(x)=\log(6)+2\log(a)\]
\[\log(x)=\frac{1}{2}\log(6)+\log(a)\]

Answer 16

i see thanks you guys!!

Answer 17

np.