What is expand log_{10}((a^4)/(b^2c^3)) ?

The solution to expand log_{10}((a^4)/(b^2c^3)) is 4log_{10}(a)-2log_{10}(b)-3log_{10}(c)

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expand log_{10}((a^4)/(b^2c^3))

expand

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

4 lo g_{10} (a) - 2 lo g_{10} (b) - 3 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

Apply log rule:

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

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}}) = lo g_{10} (a^{4}) - lo g_{10} (b^{2} c^{3})

= lo g_{10} (a^{4}) - lo g_{10} (b^{2} c^{3})

Apply log rule:

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

lo g_{10} (a^{4}) = 4 lo g_{10} (a)

= 4 lo g_{10} (a) - lo g_{10} (b^{2} c^{3})

Apply log rule:

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

lo g_{10} (b^{2} c^{3}) = lo g_{10} (b^{2}) + lo g_{10} (c^{3})

= 4 lo g_{10} (a) - (lo g_{10} (b^{2}) + lo g_{10} (c^{3}))

Apply log rule:

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

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

= 4 lo g_{10} (a) - (2 lo g_{10} (b) + lo g_{10} (c^{3}))

Apply log rule:

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

lo g_{10} (c^{3}) = 3 lo g_{10} (c)

= 4 lo g_{10} (a) - (2 lo g_{10} (b) + 3 lo g_{10} (c))

- (2 lo g_{10} (b) + 3 lo g_{10} (c)) : - 2 lo g_{10} (b) - 3 lo g_{10} (c)

= 4 lo g_{10} (a) - 2 lo g_{10} (b) - 3 lo g_{10} (c)

ln (θ (θ + 1) x^{θ - 1} (1 - x))

300 ln (\frac{1}{2})

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

ln (\frac{1}{2}) + \frac{π}{6}

3 ln (a) + 2 ln (b)

What is expand log_{10}((a^4)/(b^2c^3)) ?
The solution to expand log_{10}((a^4)/(b^2c^3)) is 4log_{10}(a)-2log_{10}(b)-3log_{10}(c)