What is the answer to log_{8}(x^3)-log_{x}(8)=2 ?

The answer to log_{8}(x^3)-log_{x}(8)=2 is x=8,x= 1/2

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log_{8}(x^3)-log_{x}(8)=2

lo g_{8} (x^{3}) - lo g_{x} (8) = 2

x = 8, x = \frac{1}{2}

Decimal Notation

x = 8, x = 0.5

Solution steps

lo g_{8} (x^{3}) - lo g_{x} (8) = 2

Apply log rules

3 lo g_{8} (x) - \frac{1}{lo g _{8} ( x )} = 2

Rewrite the equation with

lo g_{8} (x) = u

3 u - \frac{1}{u} = 2

Solve

3 u - \frac{1}{u} = 2 : u = 1, u = - \frac{1}{3}

u = 1, u = - \frac{1}{3}

Substitute back

u = lo g_{8} (x),

solve for

x

Solve

lo g_{8} (x) = 1 : x = 8

Solve

lo g_{8} (x) = - \frac{1}{3} : x = \frac{1}{2}

x = 8, x = \frac{1}{2}

Verify Solutions:

x = 8

True

, x = \frac{1}{2}

True

The solutions are

x = 8, x = \frac{1}{2}

20 = 20 lo g_{10} (x)

lo g_{x} (8) = - \frac{3}{2}

2 lo g_{7} (- 2 r) = 0

lo g_{10} (- 2 x) = 2 lo g_{10} (x + 1)

ln (10 x - 25) - 2 ln (x) = 0

What is the answer to log_{8}(x^3)-log_{x}(8)=2 ?
The answer to log_{8}(x^3)-log_{x}(8)=2 is x=8,x= 1/2
Solve for x: log_{8}(x^3)-log_{x}(8)=2
The solution is x=8,x= 1/2