What is the answer to log_{5}(x)=1+log_{x}(25) ?

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

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log_{5}(x)=1+log_{x}(25)

lo g_{5} (x) = 1 + lo g_{x} (25)

x = 25, x = \frac{1}{5}

Decimal Notation

x = 25, x = 0.2

Solution steps

lo g_{5} (x) = 1 + lo g_{x} (25)

Apply log rules

lo g_{5} (x) = 1 + \frac{2}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

u = 1 + \frac{2}{u}

Solve

u = 1 + \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 = \frac{1}{5}

x = 25, x = \frac{1}{5}

Verify Solutions:

x = 25

True

, x = \frac{1}{5}

True

The solutions are

x = 25, x = \frac{1}{5}

lo g_{x} (8 x - 15) = 2

3 ln (x) = - 6

lo g_{2} (\frac{x + 1}{x - 1}) = 3

ln (7 x - 12) = 2 ln (x)

lo g_{b} (1000) = 3

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