What is expand log_{10}((4(8+x)^2)/(x^5)) ?

The solution to expand log_{10}((4(8+x)^2)/(x^5)) is 2log_{10}(2)+2log_{10}(8+x)-5log_{10}(x)

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expand log_{10}((4(8+x)^2)/(x^5))

expand

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}})

2 lo g_{10} (2) + 2 lo g_{10} (8 + x) - 5 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}})

Apply log rule:

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

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}}) = lo g_{10} (4 (8 + x)^{2}) - lo g_{10} (x^{5})

= lo g_{10} (4 (x + 8)^{2}) - lo g_{10} (x^{5})

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= lo g_{10} (4 (8 + x)^{2}) - 5 lo g_{10} (x)

Apply log rule:

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

lo g_{10} (4 (8 + x)^{2}) = lo g_{10} (4) + lo g_{10} ((8 + x)^{2})

= lo g_{10} (4) + lo g_{10} ((x + 8)^{2}) - 5 lo g_{10} (x)

Apply log rule:

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

lo g_{10} ((8 + x)^{2}) = 2 lo g_{10} (8 + x)

= lo g_{10} (4) + 2 lo g_{10} (8 + x) - 5 lo g_{10} (x)

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) + 2 lo g_{10} (x + 8) - 5 lo g_{10} (x)

- ln (2) - m + m ln (m + 1) + ln (m + 1) + 1

- 0.7 \cdot lo g_{2} (0.7) - (1 - 0.7) \cdot lo g_{2} (1 - 0.7)

- 0.8436 ln (\frac{1}{12})

3 lo g_{m} (y) - \frac{1}{3} lo g_{m} (x) + 6 lo g_{m} (w)

ln (\frac{x + 3}{x + 1})

What is expand log_{10}((4(8+x)^2)/(x^5)) ?
The solution to expand log_{10}((4(8+x)^2)/(x^5)) is 2log_{10}(2)+2log_{10}(8+x)-5log_{10}(x)