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

The answer to log_{4}(x-4)=1-log_{4}(x) is x=2(1+sqrt(2))

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

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

x = 2 (1 + 2)

Solution steps

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

Add

lo g_{4} (x)

to both sides

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

Simplify

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

Apply log rules

(x - 4) x = 4

Solve

(x - 4) x = 4 : x = 2 (1 + 2), x = 2 (1 - 2)

x = 2 (1 + 2), x = 2 (1 - 2)

Verify Solutions:

x = 2 (1 + 2)

True

, x = 2 (1 - 2)

False

The solution is

x = 2 (1 + 2)

lo g_{3} (9 x) = 5 - lo g_{3} (8)

y, lo g_{e} (y) = x

lo g_{2} (- 4 x^{2} + 12 x) = 3

0.21 = 0.0592 ln (x)

lo g_{4} (y) - lo g_{4} (9) = 3

What is the answer to log_{4}(x-4)=1-log_{4}(x) ?
The answer to log_{4}(x-4)=1-log_{4}(x) is x=2(1+sqrt(2))
Solve for x: log_{4}(x-4)=1-log_{4}(x)
The solution is x=2(1+sqrt(2))