What is 2log_{10}(x)-3+log_{10}(x/(10)) ?

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

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simplify 2log_{10}(x)-3+log_{10}(x/(10))

simplify

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

3 lo g_{10} (x) - 4

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Simplify

lo g_{10} (x^{2}) + lo g_{10} (\frac{x}{10}) : lo g_{10} (\frac{x ^{3}}{10})

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

Simplify

lo g_{10} (\frac{x ^{3}}{10}) : 3 lo g_{10} (x) - 1

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

Apply rule:

(a) = a

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

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

Subtract the numbers:

- 1 - 3 = - 4

= 3 lo g_{10} (x) - 4

lo g_{8} (14 x)

3 lo g_{10} (x) + 2 lo g_{10} (y) - lo g_{10} (z)

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

lo g_{g} (\frac{s t ^{6}}{r ^{7}})

What is 2log_{10}(x)-3+log_{10}(x/(10)) ?
The solution to 2log_{10}(x)-3+log_{10}(x/(10)) is 3log_{10}(x)-4