What is the answer to log_{10}(x-3)=1-log_{10}(x) ?

The answer to log_{10}(x-3)=1-log_{10}(x) is x=5

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log_{10}(x-3)=1-log_{10}(x)

lo g_{10} (x - 3) = 1 - lo g_{10} (x)

x = 5

Solution steps

lo g_{10} (x - 3) = 1 - lo g_{10} (x)

Add

lo g_{10} (x)

to both sides

lo g_{10} (x - 3) + lo g_{10} (x) = 1 - lo g_{10} (x) + lo g_{10} (x)

Simplify

lo g_{10} (x - 3) + lo g_{10} (x) = 1

Apply log rules

(x - 3) x = 10

Solve

(x - 3) x = 10 : x = 5, x = - 2

x = 5, x = - 2

Verify Solutions:

x = 5

True

, x = - 2

False

The solution is

x = 5

lo g_{10} (16 x) - lo g_{10} (2) = lo g_{10} (32)

lo g_{x} (\frac{1}{8}) = - 1.5

\frac{lo g _{10} ( 2 x )}{lo g _{10} ( 14 )} = 1

- lo g_{a} (x)

5 = x^{3} lo g_{1} (x)

What is the answer to log_{10}(x-3)=1-log_{10}(x) ?
The answer to log_{10}(x-3)=1-log_{10}(x) is x=5
Solve for x: log_{10}(x-3)=1-log_{10}(x)
The solution is x=5