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

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

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

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

x = 25

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

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

Apply log rules

(x - 21) x = 100

Solve

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

x = 25, x = - 4

Verify Solutions:

x = 25

True

, x = - 4

False

The solution is

x = 25

lo g_{5} (x + 2) = 1 - lo g_{5} (x + 6)

0.32 = ln (x)

9 ln (x) = 1

ln (x^{8}) - ln (x^{3}) = 5

2 ln (x - 1) = 0

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