What is expand log_{10}(C*x^a*y^b) ?

The solution to expand log_{10}(C*x^a*y^b) is log_{10}(C)+alog_{10}(x)+blog_{10}(y)

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expand log_{10}(Cx^ay^b)

expand

lo g_{10} (C \cdot x^{a} \cdot y^{b})

lo g_{10} (C) + a lo g_{10} (x) + b lo g_{10} (y)

Solution steps

lo g_{10} (C x^{a} y^{b})

Apply log rule:

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

lo g_{10} (C x^{a} y^{b}) = lo g_{10} (C) + lo g_{10} (x^{a}) + lo g_{10} (y^{b})

= lo g_{10} (C) + lo g_{10} (x^{a}) + lo g_{10} (y^{b})

Apply log rule:

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

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

= lo g_{10} (C) + a lo g_{10} (x) + lo g_{10} (y^{b})

Apply log rule:

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

lo g_{10} (y^{b}) = b lo g_{10} (y)

= lo g_{10} (C) + a lo g_{10} (x) + b lo g_{10} (y)

lo g_{2} (\frac{( 6 x y )}{x ^{2}})

- lo g_{10} (1.67 \cdot 1 0^{- 5})

ln ((7 x^{3} + 3)^{c o s (x)})

lo g_{10} ((\frac{u ^{6}}{v})^{4})

ln (x - 4) [ln (x - 5) + ln (x + 5)]

What is expand log_{10}(C*x^a*y^b) ?
The solution to expand log_{10}(C*x^a*y^b) is log_{10}(C)+alog_{10}(x)+blog_{10}(y)