What is the answer to log_{5}(25x)+log_{x}(5)=4 ?

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

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log_{5}(25x)+log_{x}(5)=4

lo g_{5} (25 x) + lo g_{x} (5) = 4

x = 5

Solution steps

lo g_{5} (25 x) + lo g_{x} (5) = 4

Apply log rules

lo g_{5} (25) + lo g_{5} (x) + \frac{1}{lo g _{5} ( x )} = 4

Rewrite the equation with

lo g_{5} (x) = u

lo g_{5} (25) + u + \frac{1}{u} = 4

Solve

lo g_{5} (25) + u + \frac{1}{u} = 4 : u = 1

u = 1

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 1 : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{5} (11 - 6 x) = lo g_{5} (1 - x)

2 ln (x - 1) + 6 = 8

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

ln (x + 1) = 1.86

lo g_{10} (x) + lo g_{10} (2 x) = 5

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