What is the answer to 3log_{8}(x)=2log_{x}(8)+5 ?

The answer to 3log_{8}(x)=2log_{x}(8)+5 is x=64,x= 1/2

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3log_{8}(x)=2log_{x}(8)+5

3 lo g_{8} (x) = 2 lo g_{x} (8) + 5

x = 64, x = \frac{1}{2}

Decimal Notation

x = 64, x = 0.5

Solution steps

3 lo g_{8} (x) = 2 lo g_{x} (8) + 5

Apply log rules

3 lo g_{8} (x) = \frac{2}{lo g _{8} ( x )} + 5

Rewrite the equation with

lo g_{8} (x) = u

3 u = \frac{2}{u} + 5

Solve

3 u = \frac{2}{u} + 5 : u = 2, u = - \frac{1}{3}

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

Substitute back

u = lo g_{8} (x),

solve for

x

Solve

lo g_{8} (x) = 2 : x = 64

Solve

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

x = 64, x = \frac{1}{2}

Verify Solutions:

x = 64

True

, x = \frac{1}{2}

True

The solutions are

x = 64, x = \frac{1}{2}

0.26 = ln (y)

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

lo g_{x} (6 - 5 x) = 2

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

7.5 = - lo g_{10} (x)

What is the answer to 3log_{8}(x)=2log_{x}(8)+5 ?
The answer to 3log_{8}(x)=2log_{x}(8)+5 is x=64,x= 1/2
Solve for x: 3log_{8}(x)=2log_{x}(8)+5
The solution is x=64,x= 1/2