What is the answer to 3^{log_{x}(81)}=x ?

The answer to 3^{log_{x}(81)}=x is x=9,x= 1/9

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3^{log_{x}(81)}=x

3^{l o g_{x} (81)} = x

x = 9, x = \frac{1}{9}

Solution steps

3^{l o g_{x} (81)} = x

Apply log rules

\frac{ln ( 8 1 ^{l o g_{x} (3)} )}{ln ( x )} = 1

Multiply both sides by

ln (x)

\frac{ln ( 8 1 ^{l o g_{x} (3)} )}{ln ( x )} ln (x) = 1 \cdot ln (x)

Simplify

ln (8 1^{l o g_{x} (3)}) = ln (x)

Apply log rules

4 lo g_{x} (3) lo g_{x} (3) = 1

Rewrite the equation with

lo g_{x} (3) = u

4 uu = 1

Solve

4 uu = 1 : u = \frac{1}{4}, u = - \frac{1}{4}

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

Substitute back

u = lo g_{x} (3),

solve for

x

Solve

lo g_{x} (3) = \frac{1}{4} : x = 9

Solve

lo g_{x} (3) = - \frac{1}{4} : x = \frac{1}{9}

x = 9, x = \frac{1}{9}

Verify Solutions:

x = 9

True

, x = \frac{1}{9}

True

The solutions are

x = 9, x = \frac{1}{9}

lo g_{x} (625) = - 4

lo g_{9} (2 x) - lo g_{3} (2) = 1

lo g_{3} (4 x - 2) = 4

lo g_{2} (x) = 10000000

0.83 = ln (y)

What is the answer to 3^{log_{x}(81)}=x ?
The answer to 3^{log_{x}(81)}=x is x=9,x= 1/9
Solve for x: 3^{log_{x}(81)}=x
The solution is x=9,x= 1/9