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

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

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

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

y = 25

Solution steps

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

Add

lo g_{10} (y - 21)

to both sides

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

Simplify

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

Apply log rules

y (y - 21) = 100

Solve

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

y = 25, y = - 4

Verify Solutions:

y = 25

True

, y = - 4

False

The solution is

y = 25

lo g_{6} (5 x) - lo g_{6} (4) = 0

x ln (1) = ln (x)

ln (x) = ln (7)

ln (x) = - 0.432

lo g_{5} (5^{x}) = lo g_{5} (1)

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