What is the answer to log_{5}(x)-1=6log_{x}(5) ?

The answer to log_{5}(x)-1=6log_{x}(5) is x=125,x= 1/25

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log_{5}(x)-1=6log_{x}(5)

lo g_{5} (x) - 1 = 6 lo g_{x} (5)

x = 125, x = \frac{1}{25}

Decimal

x = 125, x = 0.04

Solution steps

lo g_{5} (x) - 1 = 6 lo g_{x} (5)

Apply log rules

lo g_{5} (x) - 1 = \frac{6}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

u - 1 = \frac{6}{u}

Solve

u - 1 = \frac{6}{u} : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

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

x = 125, x = \frac{1}{25}

Verify Solutions:

x = 125

True

, x = \frac{1}{25}

True

The solutions are

x = 125, x = \frac{1}{25}

ln ((x + 2)^{2}) = 6

lo g_{4} (3 x - 4) + lo g_{4} (x + 6) = 2

lo g_{3} (x + 7) = 4

lo g_{x} (5 x) - lo g_{6} (4) = 0

lo g_{2} (x + 5) = 6 - x

What is the answer to log_{5}(x)-1=6log_{x}(5) ?
The answer to log_{5}(x)-1=6log_{x}(5) is x=125,x= 1/25
Solve for x: log_{5}(x)-1=6log_{x}(5)
The solution is x=125,x= 1/25