What is the answer to log_{x}(3x)=2 ?

The answer to log_{x}(3x)=2 is x=3

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log_{x}(3x)=2

lo g_{x} (3 x) = 2

x = 3

Solution steps

lo g_{x} (3 x) = 2

Apply log rules

\frac{ln ( 3 x )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 3 x )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (3 x) = 2 ln (x)

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{6} (2 x - 5) + 4 = 18

lo g_{7} (x - 9) = 2

lo g_{3} (5 + x) = 4

lo g_{2} (x^{2}) + 4 = 10

ln (x + 2) + ln (x) = ln (24)