What is the answer to log_{5}(x)+12log_{x}(5)=7 ?

The answer to log_{5}(x)+12log_{x}(5)=7 is x=625,x=125

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log_{5}(x)+12log_{x}(5)=7

lo g_{5} (x) + 12 lo g_{x} (5) = 7

x = 625, x = 125

Solution steps

lo g_{5} (x) + 12 lo g_{x} (5) = 7

Apply log rules

lo g_{5} (x) + \frac{12}{lo g _{5} ( x )} = 7

Rewrite the equation with

lo g_{5} (x) = u

u + \frac{12}{u} = 7

Solve

u + \frac{12}{u} = 7 : u = 4, u = 3

u = 4, u = 3

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

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

x = 625, x = 125

Verify Solutions:

x = 625

True

, x = 125

True

The solutions are

x = 625, x = 125

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

ln (x) - x = - 2

ln (x + 5) = 2 + ln (x)

lo g_{0.5}^{2} (1 - x^{2}) = 4

1.5 = - lo g_{10} (x)

What is the answer to log_{5}(x)+12log_{x}(5)=7 ?
The answer to log_{5}(x)+12log_{x}(5)=7 is x=625,x=125
Solve for x: log_{5}(x)+12log_{x}(5)=7
The solution is x=625,x=125