What is the answer to log_{3}(x)=64log_{x}(3) ?

The answer to log_{3}(x)=64log_{x}(3) is x=6561,x= 1/6561

Solve for x: log_{3}(x)=64log_{x}(3)

The solution is x=6561,x= 1/6561

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lo g_{3} (x) = 64 lo g_{x} (3)

x = 6561, x = \frac{1}{6561}

Decimal Notation

x = 6561, x = 0.00015 \dots

Solution steps

lo g_{3} (x) = 64 lo g_{x} (3)

Apply log rules

lo g_{3} (x) = \frac{64}{lo g _{3} ( x )}

Rewrite the equation with

lo g_{3} (x) = u

u = \frac{64}{u}

Solve

u = \frac{64}{u} : u = 8, u = - 8

u = 8, u = - 8

Substitute back

u = lo g_{3} (x),

solve for

x

Solve

lo g_{3} (x) = 8 : x = 6561

Solve

lo g_{3} (x) = - 8 : x = \frac{1}{6561}

x = 6561, x = \frac{1}{6561}

Verify Solutions:

x = 6561

True

, x = \frac{1}{6561}

True

The solutions are

x = 6561, x = \frac{1}{6561}

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

2 ln (x - 2) + ln (x + 8) = 3 ln (x)

lo g_{5} (y) = - 3

ln (x) = ln (x - 2000) + 14876

- 4 ln (5 x + 2) = 11

What is the answer to log_{3}(x)=64log_{x}(3) ?
The answer to log_{3}(x)=64log_{x}(3) is x=6561,x= 1/6561
Solve for x: log_{3}(x)=64log_{x}(3)
The solution is x=6561,x= 1/6561