What is the answer to 6log_{x}(25)=7-log_{5}(x) ?

The answer to 6log_{x}(25)=7-log_{5}(x) is x=125,x=625

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6log_{x}(25)=7-log_{5}(x)

6 lo g_{x} (25) = 7 - lo g_{5} (x)

x = 125, x = 625

Solution steps

6 lo g_{x} (25) = 7 - lo g_{5} (x)

Apply log rules

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

Rewrite the equation with

lo g_{5} (x) = u

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

Solve

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

u = 3, u = 4

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

Solve

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

x = 125, x = 625

Verify Solutions:

x = 125

True

, x = 625

True

The solutions are

x = 125, x = 625

0.52 = ln (y)

lo g_{x} (2) = 3

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

ln (3 - 2 x) = - 4

0.72 = lo g_{10} (x)

What is the answer to 6log_{x}(25)=7-log_{5}(x) ?
The answer to 6log_{x}(25)=7-log_{5}(x) is x=125,x=625
Solve for x: 6log_{x}(25)=7-log_{5}(x)
The solution is x=125,x=625