What is the answer to log_{5}(x)=4log_{x}(5)+3 ?

The answer to log_{5}(x)=4log_{x}(5)+3 is x=625,x= 1/5

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log_{5}(x)=4log_{x}(5)+3

lo g_{5} (x) = 4 lo g_{x} (5) + 3

x = 625, x = \frac{1}{5}

Decimal Notation

x = 625, x = 0.2

Solution steps

lo g_{5} (x) = 4 lo g_{x} (5) + 3

Apply log rules

lo g_{5} (x) = \frac{4}{lo g _{5} ( x )} + 3

Rewrite the equation with

lo g_{5} (x) = u

u = \frac{4}{u} + 3

Solve

u = \frac{4}{u} + 3 : u = 4, u = - 1

u = 4, u = - 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

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

x = 625, x = \frac{1}{5}

Verify Solutions:

x = 625

True

, x = \frac{1}{5}

True

The solutions are

x = 625, x = \frac{1}{5}

ln (5 x - 4) - ln (7) = ln (37)

lo g_{x} (48) = 2

lo g_{e} (3 x + 5) + lo g_{e} (2) = 2

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

ln (x + e^{2}) = 0

What is the answer to log_{5}(x)=4log_{x}(5)+3 ?
The answer to log_{5}(x)=4log_{x}(5)+3 is x=625,x= 1/5
Solve for x: log_{5}(x)=4log_{x}(5)+3
The solution is x=625,x= 1/5