What is the answer to 12log_{x}(5)=3log_{5}(x) ?

The answer to 12log_{x}(5)=3log_{5}(x) is x=25,x= 1/25

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12log_{x}(5)=3log_{5}(x)

12 lo g_{x} (5) = 3 lo g_{5} (x)

x = 25, x = \frac{1}{25}

Decimal Notation

x = 25, x = 0.04

Solution steps

12 lo g_{x} (5) = 3 lo g_{5} (x)

Divide both sides by

3

\frac{12 lo g _{x} ( 5 )}{3} = \frac{3 lo g _{5} ( x )}{3}

Simplify

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

Apply log rules

\frac{4}{lo g _{5} ( x )} = lo g_{5} (x)

Rewrite the equation with

lo g_{5} (x) = u

\frac{4}{u} = u

Solve

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

u = 2, u = - 2

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 2 : x = 25

Solve

lo g_{5} (x) = - 2 : x = \frac{1}{25}

x = 25, x = \frac{1}{25}

Verify Solutions:

x = 25

True

, x = \frac{1}{25}

True

The solutions are

x = 25, x = \frac{1}{25}

lo g_{10} (4 x + 1) = lo g_{10} (x + 2)

lo g_{10} (2 x - 100) = 3

0.69 = ln (y)

lo g_{10} (m) + lo g_{10} (m - 3) = 1

ln (x - 2) + ln (3) = 5

What is the answer to 12log_{x}(5)=3log_{5}(x) ?
The answer to 12log_{x}(5)=3log_{5}(x) is x=25,x= 1/25
Solve for x: 12log_{x}(5)=3log_{5}(x)
The solution is x=25,x= 1/25