What is the answer to 16log_{x}(3)=log_{3}(x) ?

The answer to 16log_{x}(3)=log_{3}(x) is x=81,x= 1/81

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16log_{x}(3)=log_{3}(x)

16 lo g_{x} (3) = lo g_{3} (x)

x = 81, x = \frac{1}{81}

Decimal

x = 81, x = 0.01234 \dots

Solution steps

16 lo g_{x} (3) = lo g_{3} (x)

Apply log rules

\frac{16}{lo g _{3} ( x )} = lo g_{3} (x)

Rewrite the equation with

lo g_{3} (x) = u

\frac{16}{u} = u

Solve

\frac{16}{u} = u : u = 4, u = - 4

u = 4, u = - 4

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 4 : x = 81

Solve

lo g_{3} (x) = - 4 : x = \frac{1}{81}

x = 81, x = \frac{1}{81}

Verify Solutions:

x = 81

True

, x = \frac{1}{81}

True

The solutions are

x = 81, x = \frac{1}{81}

ln (4) + ln (x + 3) = - 3

lo g_{2} (x - 2) + lo g_{2} (x + 5) = 1

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

ln (a) = ln (3 e^{2}) - 2

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

What is the answer to 16log_{x}(3)=log_{3}(x) ?
The answer to 16log_{x}(3)=log_{3}(x) is x=81,x= 1/81
Solve for x: 16log_{x}(3)=log_{3}(x)
The solution is x=81,x= 1/81