What is expand log_{10}((sqrt(x+10))/(10x^2)) ?

The solution to expand log_{10}((sqrt(x+10))/(10x^2)) is log_{10}(sqrt(x+10))-1-2log_{10}(x)

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expand log_{10}((sqrt(x+10))/(10x^2))

expand

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

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

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

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

ln (\frac{a ^{2} b ^{4}}{c ^{8}})

ln (\frac{47}{50}) + (0.085)

ln (\frac{( x + 2 ) ^{7}}{x ^{5}})

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t)

- lo g_{10} (1.8 \cdot 10)

What is expand log_{10}((sqrt(x+10))/(10x^2)) ?
The solution to expand log_{10}((sqrt(x+10))/(10x^2)) is log_{10}(sqrt(x+10))-1-2log_{10}(x)