Question

What is the solution to the equation
?

Answer 1

Answer:        $x=9$

Step-by-step explanation:

Alright, lets get started.

$log_{6}4x^2-log_{6}x=2$

Using the property of logs : $log (m) - log(n)=log\frac{m}{n}$

$log_{6}\frac{4x^2}{x}=2$

$log_{6}4x=2$

Using the property of logs : $if \ log_{a}m=n, \ then \ a^n=m$

So,

$6^2=4x$

$4x=36$

Dividing 4 in both sides

$x=9$   ......................   Answer

Hope it will help :)

Answer 2

Answer:

x = 9

Step-by-step explanation:

Determine the defined range

$log^6 (4x^2) - log^6 (x) = 2, x = (0, + ∞)$

Use log^a (x) - log^a (y) = log^a (x/y) to simplify the expression

$log6 (\frac{4x^{2} }{x} )= 2$

Simplify the expression

log^6 (4x) = 2

Convert the logarithm into an exponential form using the fact that log^a (x) = b is equal to x = a^b

$4x=6^{2}$

Evaluate the power

4x = 36

Divide both sides of the equation by 4

x = 9, x = (0, + ∞)

Check if the solution is the defined range

x = 9