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

The answer to log_{10}(x)=2-log_{10}(x-21) is x=25

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

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

x = 25

Solution steps

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

Add

lo g_{10} (x - 21)

to both sides

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

Simplify

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

Apply log rules

x (x - 21) = 100

Solve

x (x - 21) = 100 : x = 25, x = - 4

x = 25, x = - 4

Verify Solutions:

x = 25

True

, x = - 4

False

The solution is

x = 25

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

0.234 = ln (x^{2})

ln (x) = 2.021

lo g_{2} (x) - lo g_{8} (x) = 6

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

What is the answer to log_{10}(x)=2-log_{10}(x-21) ?
The answer to log_{10}(x)=2-log_{10}(x-21) is x=25
Solve for x: log_{10}(x)=2-log_{10}(x-21)
The solution is x=25