What is the answer to log_{2}(x+2)=1+log_{2}(2x-4) ?

The answer to log_{2}(x+2)=1+log_{2}(2x-4) is x= 10/3

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log_{2}(x+2)=1+log_{2}(2x-4)

lo g_{2} (x + 2) = 1 + lo g_{2} (2 x - 4)

x = \frac{10}{3}

Decimal Notation

x = 3.33333 \dots

Solution steps

lo g_{2} (x + 2) = 1 + lo g_{2} (2 x - 4)

Apply log rules

x + 2 = 2 (2 x - 4)

Solve

x + 2 = 2 (2 x - 4) : x = \frac{10}{3}

x = \frac{10}{3}

Verify Solutions:

x = \frac{10}{3}

True

The solution is

x = \frac{10}{3}

lo g_{3} (x + 1) - lo g_{3} (x) = 2

\frac{1}{3} lo g_{2} (x) = - 3

lo g_{3} (x) = 81

lo g_{2} (5 x + 7) = 3

3 ln ((x + 2)^{3}) = 9 ln (x + 2)

What is the answer to log_{2}(x+2)=1+log_{2}(2x-4) ?
The answer to log_{2}(x+2)=1+log_{2}(2x-4) is x= 10/3
Solve for x: log_{2}(x+2)=1+log_{2}(2x-4)
The solution is x= 10/3