Question

Find x if 2log3x=6

Answer 1

the 3 is a base

Answer 2

x=3

Answer 3

Did that help?

Answer 4

how did you get that?

Answer 5

Using the property of logarithm such that n log a = log a^n
log3 x^2 = log3 (x+6)
Since the logs on both the sides have same bases, they can be canceled out.
So, x^2 = x + 6
x^2 - x - 6 =0
Now, factoring by regrouping:



x^2 - 3x + 2x -6 = 0
x(x -3) + 2(x-3) = 0
(x-3) (x +2) = 0
x = 3 , x =-2
Since originally we had the term 2 log3 x..which shows that x should always be greater than 0 {Because log of negative number is not defined}
Thus, x = 3

Answer 6

hmm
log properties
power property
\[\huge\rm x \log ~y = b ---> log y^x = b \]

Answer 7

\[\huge\rm \color{red}{2} \log_3 x = 6\]
apply power property

Answer 8

so what's the answer?

Answer 9

divide both sides by 2 and start with \[\log_3(x)=3\]

Answer 10

then rewrite in equivalent exponential form as \[x=3^3\]

Answer 11

alright first we have to apply power rule \[\huge\rm \color{red}{2} \log_3 x = 6\]
\[\huge\rm \log_3 x^\color{Red}{2} = 6\]

Answer 12

or you can do it that way, but you don't need to use that property of the log
dividing by 2 works also

Answer 13

now change log to exponential form