What is the answer to log_{x}(16)=log_{2}(x) ?

The answer to log_{x}(16)=log_{2}(x) is x=4,x= 1/4

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log_{x}(16)=log_{2}(x)

lo g_{x} (16) = lo g_{2} (x)

x = 4, x = \frac{1}{4}

Decimal Notation

x = 4, x = 0.25

Solution steps

lo g_{x} (16) = lo g_{2} (x)

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

\frac{4}{u} = u

Solve

\frac{4}{u} = u : u = 2, u = - 2

u = 2, u = - 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 2 : x = 4

Solve

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

x = 4, x = \frac{1}{4}

Verify Solutions:

x = 4

True

, x = \frac{1}{4}

True

The solutions are

x = 4, x = \frac{1}{4}

ln (x) = \frac{6907756}{1000000}

lo g_{10} (x - 2) = 1

4 + 2 lo g_{3} (x) = 17

4 ln (x) - 8 = 12

2 lo g_{10} (x) = lo g_{10} (64)

What is the answer to log_{x}(16)=log_{2}(x) ?
The answer to log_{x}(16)=log_{2}(x) is x=4,x= 1/4
Solve for x: log_{x}(16)=log_{2}(x)
The solution is x=4,x= 1/4