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

The solution to log_{10}((10)/x)-2-2log_{10}(x) is -3log_{10}(x)-1

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

simplify

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

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

Solution steps

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

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

Simplify

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

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

Simplify

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

= (1 - 3 lo g_{10} (x)) - 2

Apply rule:

(a) = a

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

= 1 - 3 lo g_{10} (x) - 2

Group like terms

= - 3 lo g_{10} (x) + 1 - 2

Subtract the numbers:

1 - 2 = - 1

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

lo g_{10} (\frac{5}{x})

ln (x^{5} 7 - x)

lo g_{4} (x^{2} - 25) - lo g_{4} (x - 5)

lo g_{10} (x) - 5 lo g_{10} (y) + 7 lo g_{10} (z)

- [- \frac{3}{10} ln (3) + \frac{8}{35} ln (8) + \frac{15}{14} ln (1)]

What is log_{10}((10)/x)-2-2log_{10}(x) ?
The solution to log_{10}((10)/x)-2-2log_{10}(x) is -3log_{10}(x)-1