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

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

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

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

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

Decimal Notation

x = 125, x = 0.008

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{5} (x) = u

u = \frac{9}{u}

Solve

u = \frac{9}{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}

lo g_{2} (x + 6) + lo g_{2} (x + 7) = 1

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

lo g_{2} (n) = 4

ln (x) + ln (x + 2) = ln (15)

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

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