What is the answer to log_{1/2}(x)-log_{1/2}(3-x)=0 ?

The answer to log_{1/2}(x)-log_{1/2}(3-x)=0 is x= 3/2

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log_{1/2}(x)-log_{1/2}(3-x)=0

lo g_{\frac{1}{2}} (x) - lo g_{\frac{1}{2}} (3 - x) = 0

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

lo g_{\frac{1}{2}} (x) - lo g_{\frac{1}{2}} (3 - x) = 0

Add

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

to both sides

lo g_{\frac{1}{2}} (x) - lo g_{\frac{1}{2}} (3 - x) + lo g_{\frac{1}{2}} (3 - x) = 0 + lo g_{\frac{1}{2}} (3 - x)

Simplify

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

Apply log rules

x = 3 - x

Solve

x = 3 - x : x = \frac{3}{2}

x = \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

The solution is

x = \frac{3}{2}

2 lo g_{10} (x) = 6 lo g_{2} (x)

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

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

ln (8 x + 5) = 2 + 2 ln^{3} (x)

p, lo g_{10} (p (x)^{2}) + lo g_{10} (p) (x - 1) = 0

What is the answer to log_{1/2}(x)-log_{1/2}(3-x)=0 ?
The answer to log_{1/2}(x)-log_{1/2}(3-x)=0 is x= 3/2
Solve for x: log_{1/2}(x)-log_{1/2}(3-x)=0
The solution is x= 3/2