What is the answer to log_{4x}(3)=2 ?

The answer to log_{4x}(3)=2 is x=(sqrt(3))/4

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log_{4x}(3)=2

lo g_{4 x} (3) = 2

x = \frac{3}{4}

Decimal

x = 0.43301 \dots

Solution steps

lo g_{4 x} (3) = 2

Apply log rules

\frac{1}{lo g _{3} ( 4 x )} = 2

Multiply both sides by

lo g_{3} (4 x)

\frac{1}{lo g _{3} ( 4 x )} lo g_{3} (4 x) = 2 lo g_{3} (4 x)

Simplify

1 = 2 lo g_{3} (4 x)

Switch sides

2 lo g_{3} (4 x) = 1

Divide both sides by

2

lo g_{3} (4 x) = \frac{1}{2}

Apply log rules

4 x = 3

Solve

4 x = 3 : x = \frac{3}{4}

x = \frac{3}{4}

Verify Solutions:

x = \frac{3}{4}

True

The solution is

x = \frac{3}{4}

lo g_{10} (x) = \frac{1}{2}

lo g_{2} (x) - lo g_{2} (x - 3) = 1

ln (4 x^{2} - 4 x + 1) = 0

2 ln (x) = ln (x^{2})

ln (x) = 1 - ln (x + 3)

What is the answer to log_{4x}(3)=2 ?
The answer to log_{4x}(3)=2 is x=(sqrt(3))/4
Solve for x: log_{4x}(3)=2
The solution is x=(sqrt(3))/4