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

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

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

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

x = 5

Solution steps

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

Add

lo g_{10} (x - 3)

to both sides

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

Simplify

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

Apply log rules

x (x - 3) = 10

Solve

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

x = 5, x = - 2

Verify Solutions:

x = 5

True

, x = - 2

False

The solution is

x = 5

ln (x) + ln (x - 4) = ln (4)

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

lo g_{7} (x^{2} - 9) = 1

ln (y) = 5

lo g_{2} (6) + 3 \cdot lo g_{2} (p) = 3

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