What is the answer to log_{3}(x)=3+2log_{x}(9) ?

The answer to log_{3}(x)=3+2log_{x}(9) is x=81,x= 1/3

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log_{3}(x)=3+2log_{x}(9)

lo g_{3} (x) = 3 + 2 lo g_{x} (9)

x = 81, x = \frac{1}{3}

Solution steps

lo g_{3} (x) = 3 + 2 lo g_{x} (9)

Apply log rules

lo g_{3} (x) = 3 + \frac{4}{lo g _{3} ( x )}

Rewrite the equation with

lo g_{3} (x) = u

u = 3 + \frac{4}{u}

Solve

u = 3 + \frac{4}{u} : u = 4, u = - 1

u = 4, u = - 1

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 4 : x = 81

Solve

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

x = 81, x = \frac{1}{3}

Verify Solutions:

x = 81

True

, x = \frac{1}{3}

True

The solutions are

x = 81, x = \frac{1}{3}

ln (x + 5) + ln (x - 1) = 2

2 lo g_{10} (x) = - 10

lo g_{10} (x) = 0.2293300000000 \dots

lo g_{2} (x) = lo g_{4} (3)

lo g_{3} (2 x + 5) = 1

What is the answer to log_{3}(x)=3+2log_{x}(9) ?
The answer to log_{3}(x)=3+2log_{x}(9) is x=81,x= 1/3
Solve for x: log_{3}(x)=3+2log_{x}(9)
The solution is x=81,x= 1/3