What is the answer to log_{5}(x)=16log_{x}(5) ?

The answer to log_{5}(x)=16log_{x}(5) is x=625,x= 1/625

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log_{5}(x)=16log_{x}(5)

lo g_{5} (x) = 16 lo g_{x} (5)

x = 625, x = \frac{1}{625}

Decimal Notation

x = 625, x = 0.0016

Solution steps

lo g_{5} (x) = 16 lo g_{x} (5)

Apply log rules

lo g_{5} (x) = \frac{16}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

u = \frac{16}{u}

Solve

u = \frac{16}{u} : u = 4, u = - 4

u = 4, u = - 4

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 4 : x = 625

Solve

lo g_{5} (x) = - 4 : x = \frac{1}{625}

x = 625, x = \frac{1}{625}

Verify Solutions:

x = 625

True

, x = \frac{1}{625}

True

The solutions are

x = 625, x = \frac{1}{625}

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

2 lo g_{10} (x) ln (10) = ln (4)

lo g_{3} (x^{2} - 8 x) = 2

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

ln ((x - 2)^{2}) - ln (x) = 0

What is the answer to log_{5}(x)=16log_{x}(5) ?
The answer to log_{5}(x)=16log_{x}(5) is x=625,x= 1/625
Solve for x: log_{5}(x)=16log_{x}(5)
The solution is x=625,x= 1/625