What is the answer to 9log_{8}(x)=6+8log_{x}(8) ?

The answer to 9log_{8}(x)=6+8log_{x}(8) is x=16,x= 1/4

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9log_{8}(x)=6+8log_{x}(8)

9 lo g_{8} (x) = 6 + 8 lo g_{x} (8)

x = 16, x = \frac{1}{4}

Decimal Notation

x = 16, x = 0.25

Solution steps

9 lo g_{8} (x) = 6 + 8 lo g_{x} (8)

Apply log rules

9 lo g_{8} (x) = 6 + \frac{8}{lo g _{8} ( x )}

Rewrite the equation with

lo g_{8} (x) = u

9 u = 6 + \frac{8}{u}

Solve

9 u = 6 + \frac{8}{u} : u = \frac{4}{3}, u = - \frac{2}{3}

u = \frac{4}{3}, u = - \frac{2}{3}

Substitute back

u = lo g_{8} (x),

solve for

x

Solve

lo g_{8} (x) = \frac{4}{3} : x = 16

Solve

lo g_{8} (x) = - \frac{2}{3} : x = \frac{1}{4}

x = 16, x = \frac{1}{4}

Verify Solutions:

x = 16

True

, x = \frac{1}{4}

True

The solutions are

x = 16, x = \frac{1}{4}

lo g_{10} (9 x) + lo g_{10} (x) = 4

lo g_{10} (3 x) = 1.3

ln (4 x - 4) - 2 ln (x) = 0

lo g_{216} (x) = \frac{2}{3}

2 lo g_{10} (x) + 3 = 5 lo g_{10} (x)

What is the answer to 9log_{8}(x)=6+8log_{x}(8) ?
The answer to 9log_{8}(x)=6+8log_{x}(8) is x=16,x= 1/4
Solve for x: 9log_{8}(x)=6+8log_{x}(8)
The solution is x=16,x= 1/4