What is the answer to log_{2}(x)=8+9log_{x}(2) ?

The answer to log_{2}(x)=8+9log_{x}(2) is x=512,x= 1/2

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log_{2}(x)=8+9log_{x}(2)

lo g_{2} (x) = 8 + 9 lo g_{x} (2)

x = 512, x = \frac{1}{2}

Decimal Notation

x = 512, x = 0.5

Solution steps

lo g_{2} (x) = 8 + 9 lo g_{x} (2)

Apply log rules

lo g_{2} (x) = 8 + \frac{9}{lo g _{2} ( x )}

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

u = 8 + \frac{9}{u} : u = 9, u = - 1

u = 9, u = - 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 9 : x = 512

Solve

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

x = 512, x = \frac{1}{2}

Verify Solutions:

x = 512

True

, x = \frac{1}{2}

True

The solutions are

x = 512, x = \frac{1}{2}

ln (3 x - 2) + ln (x - 1) = 2 ln (x)

lo g_{5} (x) = - 1

lo g_{5} (t^{7}) = 5

lo g_{3} (x) + lo g_{3} (x + 2) = 1

lo g_{2} (lo g_{3} (x)) = - 1

What is the answer to log_{2}(x)=8+9log_{x}(2) ?
The answer to log_{2}(x)=8+9log_{x}(2) is x=512,x= 1/2
Solve for x: log_{2}(x)=8+9log_{x}(2)
The solution is x=512,x= 1/2