What is the answer to log_{4}(x-3)=1-log_{4}(x) ?

The answer to log_{4}(x-3)=1-log_{4}(x) is x=4

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log_{4}(x-3)=1-log_{4}(x)

lo g_{4} (x - 3) = 1 - lo g_{4} (x)

x = 4

Solution steps

lo g_{4} (x - 3) = 1 - lo g_{4} (x)

Add

lo g_{4} (x)

to both sides

lo g_{4} (x - 3) + lo g_{4} (x) = 1 - lo g_{4} (x) + lo g_{4} (x)

Simplify

lo g_{4} (x - 3) + lo g_{4} (x) = 1

Apply log rules

(x - 3) x = 4

Solve

(x - 3) x = 4 : x = 4, x = - 1

x = 4, x = - 1

Verify Solutions:

x = 4

True

, x = - 1

False

The solution is

x = 4

lo g_{10} (7) + lo g_{10} (x - 4) = 1

lo g_{100} (x) = \frac{1}{2}

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

- 5 + 2 ln (3 x) = 5

lo g_{2} (x + 3) = 2 - lo g_{2} (x + 6)

What is the answer to log_{4}(x-3)=1-log_{4}(x) ?
The answer to log_{4}(x-3)=1-log_{4}(x) is x=4
Solve for x: log_{4}(x-3)=1-log_{4}(x)
The solution is x=4