What is the answer to 9log_{x}(5)=log_{5}(x) ?

The answer to 9log_{x}(5)=log_{5}(x) is x=125,x= 1/125

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9log_{x}(5)=log_{5}(x)

9 lo g_{x} (5) = lo g_{5} (x)

x = 125, x = \frac{1}{125}

Decimal Notation

x = 125, x = 0.008

Solution steps

9 lo g_{x} (5) = lo g_{5} (x)

Apply log rules

\frac{9}{lo g _{5} ( x )} = lo g_{5} (x)

Rewrite the equation with

lo g_{5} (x) = u

\frac{9}{u} = u

Solve

\frac{9}{u} = u : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 3 : x = 125

Solve

lo g_{5} (x) = - 3 : x = \frac{1}{125}

x = 125, x = \frac{1}{125}

Verify Solutions:

x = 125

True

, x = \frac{1}{125}

True

The solutions are

x = 125, x = \frac{1}{125}

ln (x + 1) = 2

ln (x^{2}) = 14

2 lo g_{3} (x + 4) - lo g_{3} (9) = 2

lo g_{27} (x) = \frac{1}{3}

lo g_{10} (x) + lo g_{10} (x + 21) = 2

What is the answer to 9log_{x}(5)=log_{5}(x) ?
The answer to 9log_{x}(5)=log_{5}(x) is x=125,x= 1/125
Solve for x: 9log_{x}(5)=log_{5}(x)
The solution is x=125,x= 1/125