What is the answer to log_{4}(x)=6log_{x}(8) ?

The answer to log_{4}(x)=6log_{x}(8) is x=64,x= 1/64

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log_{4}(x)=6log_{x}(8)

lo g_{4} (x) = 6 lo g_{x} (8)

x = 64, x = \frac{1}{64}

Decimal Notation

x = 64, x = 0.015625

Solution steps

lo g_{4} (x) = 6 lo g_{x} (8)

Apply log rules

lo g_{4} (x) = \frac{9}{lo g _{4} ( x )}

Rewrite the equation with

lo g_{4} (x) = u

u = \frac{9}{u}

Solve

u = \frac{9}{u} : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 3 : x = 64

Solve

lo g_{4} (x) = - 3 : x = \frac{1}{64}

x = 64, x = \frac{1}{64}

Verify Solutions:

x = 64

True

, x = \frac{1}{64}

True

The solutions are

x = 64, x = \frac{1}{64}

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

lo g_{2} (x - 1) = lo g_{2} (4 x - 7)

0.62 = ln (x)

lo g_{x} (8) = \frac{1}{2}

lo g_{x} (2) = 4

What is the answer to log_{4}(x)=6log_{x}(8) ?
The answer to log_{4}(x)=6log_{x}(8) is x=64,x= 1/64
Solve for x: log_{4}(x)=6log_{x}(8)
The solution is x=64,x= 1/64