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

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

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log_{x}(4)=4log_{x}(x)

lo g_{x} (4) = 4 lo g_{x} (x)

x = 2

Solution steps

lo g_{x} (4) = 4 lo g_{x} (x)

Apply log rules

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

Multiply both sides by

lo g_{4} (x)

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

Simplify

1 = 4 lo g_{4} (x)

Switch sides

4 lo g_{4} (x) = 1

Divide both sides by

4

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

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{3} (x^{2} - 8) = 2

0 = 2 x ln (x) + x

123 = 10 lo g_{10} (\frac{x}{1})

lo g_{2} (x - 10) = 6

lo g_{a} (64) = 3

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