What is the answer to log_{2}(x)+21log_{x}(2)=10 ?

The answer to log_{2}(x)+21log_{x}(2)=10 is x=128,x=8

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log_{2}(x)+21log_{x}(2)=10

lo g_{2} (x) + 21 lo g_{x} (2) = 10

x = 128, x = 8

Solution steps

lo g_{2} (x) + 21 lo g_{x} (2) = 10

Apply log rules

lo g_{2} (x) + \frac{21}{lo g _{2} ( x )} = 10

Rewrite the equation with

lo g_{2} (x) = u

u + \frac{21}{u} = 10

Solve

u + \frac{21}{u} = 10 : u = 7, u = 3

u = 7, u = 3

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 7 : x = 128

Solve

lo g_{2} (x) = 3 : x = 8

x = 128, x = 8

Verify Solutions:

x = 128

True

, x = 8

True

The solutions are

x = 128, x = 8

lo g_{3} (x) + lo g_{9} (x) = 1

lo g_{3} (x) + lo g_{x} (9) = 3

lo g_{10} (2 x) = 3

ln (x + 2) = 0

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

What is the answer to log_{2}(x)+21log_{x}(2)=10 ?
The answer to log_{2}(x)+21log_{x}(2)=10 is x=128,x=8
Solve for x: log_{2}(x)+21log_{x}(2)=10
The solution is x=128,x=8