What is the answer to log_{5}(x)=3-2log_{x}(5) ?

The answer to log_{5}(x)=3-2log_{x}(5) is x=25,x=5

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log_{5}(x)=3-2log_{x}(5)

lo g_{5} (x) = 3 - 2 lo g_{x} (5)

x = 25, x = 5

Solution steps

lo g_{5} (x) = 3 - 2 lo g_{x} (5)

Apply log rules

lo g_{5} (x) = 3 - \frac{2}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

u = 3 - \frac{2}{u}

Solve

u = 3 - \frac{2}{u} : u = 2, u = 1

u = 2, u = 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

lo g_{5} (x) = 1 : x = 5

x = 25, x = 5

Verify Solutions:

x = 25

True

, x = 5

True

The solutions are

x = 25, x = 5

16 ln (x) = \frac{1}{ln ( x )}

lo g_{3} (- 2 x - 10) = 2 + lo g_{3} (6)

1.23 = \frac{0.0257}{4} ln (k)

x, ln (2 x + 1) = 2 - ln (x)

lo g_{10} (x - 2) = 1.258

What is the answer to log_{5}(x)=3-2log_{x}(5) ?
The answer to log_{5}(x)=3-2log_{x}(5) is x=25,x=5
Solve for x: log_{5}(x)=3-2log_{x}(5)
The solution is x=25,x=5