What is the answer to log_{5}(x)+6log_{x}(5)=5 ?

The answer to log_{5}(x)+6log_{x}(5)=5 is x=125,x=25

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log_{5}(x)+6log_{x}(5)=5

lo g_{5} (x) + 6 lo g_{x} (5) = 5

x = 125, x = 25

Solution steps

lo g_{5} (x) + 6 lo g_{x} (5) = 5

Apply log rules

lo g_{5} (x) + \frac{6}{lo g _{5} ( x )} = 5

Rewrite the equation with

lo g_{5} (x) = u

u + \frac{6}{u} = 5

Solve

u + \frac{6}{u} = 5 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = 3 : x = 125

Solve

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

x = 125, x = 25

Verify Solutions:

x = 125

True

, x = 25

True

The solutions are

x = 125, x = 25

ln (3 x + 1) - ln (x) = - 2

5 lo g_{7} (n) = 10

lo g_{4} (4 x) + 2 lo g_{4} (4) = 0

- lo g_{10} (x) = 11.45

ln (x) + ln (x - 8) = 3

What is the answer to log_{5}(x)+6log_{x}(5)=5 ?
The answer to log_{5}(x)+6log_{x}(5)=5 is x=125,x=25
Solve for x: log_{5}(x)+6log_{x}(5)=5
The solution is x=125,x=25