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

The answer to log_{x}(2)=4 is x=\sqrt[4]{2}

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log_{x}(2)=4

lo g_{x} (2) = 4

x = 42

Decimal

x = 1.18920 \dots

Solution steps

lo g_{x} (2) = 4

Apply log rules

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

Multiply both sides by

lo g_{2} (x)

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

Simplify

1 = 4 lo g_{2} (x)

Switch sides

4 lo g_{2} (x) = 1

Divide both sides by

4

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

Apply log rules

x = 42

Verify Solutions:

x = 42

True

The solution is

x = 42

3 lo g_{3} (x) - lo g_{3} (7 x) = 1

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

ln (2 x - 7) = 0.5

lo g_{2} (x) = 24

lo g_{2} (x) + lo g_{2} (x + 7) = 3

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