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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5 \cdot ln (\frac{5 2}{2})

lo g_{5} (\frac{z}{125})

π^{16} ln (\frac{2 + 2 9 ^{\frac{1}{2}}}{5})

4 ln (1 + \frac{9 i}{n})

\frac{1}{4} ln (\frac{1}{2})

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