What is the answer to 3log_{10}(x)-log_{10}(32)=log_{10}(x/2) ?

The answer to 3log_{10}(x)-log_{10}(32)=log_{10}(x/2) is x=4

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3log_{10}(x)-log_{10}(32)=log_{10}(x/2)

3 lo g_{10} (x) - lo g_{10} (32) = lo g_{10} (\frac{x}{2})

x = 4

Solution steps

3 lo g_{10} (x) - lo g_{10} (32) = lo g_{10} (\frac{x}{2})

Apply log rules

x^{3} = 16 x

Solve

x^{3} = 16 x : x = 0, x = - 4, x = 4

x = 0, x = - 4, x = 4

Verify Solutions:

x = 0

False

, x = - 4

False

, x = 4

True

The solution is

x = 4

- 1 = ln (x)

x + ln (x) = 0

2 \cdot lo g_{4} (k) = 4

ln (\frac{x}{5}) + 1 = 0

lo g_{10} (x) + lo g_{10} (x + 2) = 1

What is the answer to 3log_{10}(x)-log_{10}(32)=log_{10}(x/2) ?
The answer to 3log_{10}(x)-log_{10}(32)=log_{10}(x/2) is x=4
Solve for x: 3log_{10}(x)-log_{10}(32)=log_{10}(x/2)
The solution is x=4