What is the answer to log_{x}(3)+16log_{81}(x)=5 ?

The answer to log_{x}(3)+16log_{81}(x)=5 is x=3,x=\sqrt[4]{3}

Solve for x: log_{x}(3)+16log_{81}(x)=5

The solution is x=3,x=\sqrt[4]{3}

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lo g_{x} (3) + 16 lo g_{81} (x) = 5

Decimal Notation

x = 3, x = 1.31607 \dots

Solution steps

lo g_{x} (3) + 16 lo g_{81} (x) = 5

Apply log rules

\frac{1}{4 lo g _{81} ( x )} + 16 lo g_{81} (x) = 5

Rewrite the equation with

lo g_{81} (x) = u

\frac{1}{4 u} + 16 u = 5

Solve

\frac{1}{4 u} + 16 u = 5 : u = \frac{1}{4}, u = \frac{1}{16}

u = \frac{1}{4}, u = \frac{1}{16}

Substitute back

u = lo g_{81} (x),

solve for

x

Solve

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

Solve

Verify Solutions:

x = 3

True

The solutions are

lo g_{2} (9 x + 2) = 2

lo g_{10} (x) = lo g_{10} (x + 1)

2 ln (x) - ln (3 x - 2) = 0

8 1^{l o g_{10} (9 x)} = x^{2}

lo g_{3} (3 x) = 2

What is the answer to log_{x}(3)+16log_{81}(x)=5 ?
The answer to log_{x}(3)+16log_{81}(x)=5 is x=3,x=\sqrt[4]{3}
Solve for x: log_{x}(3)+16log_{81}(x)=5
The solution is x=3,x=\sqrt[4]{3}