What is the answer to 4(log_{5}(x)+log_{x}(5))=10 ?

The answer to 4(log_{5}(x)+log_{x}(5))=10 is x=25,x=sqrt(5)

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4(log_{5}(x)+log_{x}(5))=10

4 (lo g_{5} (x) + lo g_{x} (5)) = 10

x = 25, x = 5

Decimal Notation

x = 25, x = 2.23606 \dots

Solution steps

4 (lo g_{5} (x) + lo g_{x} (5)) = 10

Divide both sides by

2

\frac{4 ( lo g _{5} ( x ) + lo g _{x} ( 5 ) )}{2} = \frac{10}{2}

Simplify

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

Apply log rules

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

Rewrite the equation with

lo g_{5} (x) = u

2 (u + \frac{1}{u}) = 5

Solve

2 (u + \frac{1}{u}) = 5 : u = 2, u = \frac{1}{2}

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

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 2 : x = 25

Solve

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

x = 25, x = 5

Verify Solutions:

x = 25

True

, x = 5

True

The solutions are

x = 25, x = 5

x, y - 1 = ln (x)

ln (x) + ln (x^{2} + 1) = 8

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

5 lo g_{5} (x) + 5 = 0

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

What is the answer to 4(log_{5}(x)+log_{x}(5))=10 ?
The answer to 4(log_{5}(x)+log_{x}(5))=10 is x=25,x=sqrt(5)
Solve for x: 4(log_{5}(x)+log_{x}(5))=10
The solution is x=25,x=sqrt(5)