What is expand log_{d}((sqrt(a)b^5)/(c^7)) ?

The solution to expand log_{d}((sqrt(a)b^5)/(c^7)) is log_{d}(sqrt(a))+5log_{d}(b)-7log_{d}(c)

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expand log_{d}((sqrt(a)b^5)/(c^7))

expand

lo g_{d} (\frac{a b ^{5}}{c ^{7}})

lo g_{d} (a) + 5 lo g_{d} (b) - 7 lo g_{d} (c)

Solution steps

lo g_{d} (\frac{a b ^{5}}{c ^{7}})

Apply log rule:

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

lo g_{d} (\frac{a b ^{5}}{c ^{7}}) = lo g_{d} (a b^{5}) - lo g_{d} (c^{7})

= lo g_{d} (b^{5} a) - lo g_{d} (c^{7})

Apply log rule:

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

lo g_{d} (c^{7}) = 7 lo g_{d} (c)

= lo g_{d} (a b^{5}) - 7 lo g_{d} (c)

Apply log rule:

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

lo g_{d} (a b^{5}) = lo g_{d} (a) + lo g_{d} (b^{5})

= lo g_{d} (a) + lo g_{d} (b^{5}) - 7 lo g_{d} (c)

Apply log rule:

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

lo g_{d} (b^{5}) = 5 lo g_{d} (b)

= lo g_{d} (a) + 5 lo g_{d} (b) - 7 lo g_{d} (c)

6.1 + lo g_{10} (\frac{15}{6.7})

ln (5) + 1 + ln (y) - ln (x)

4.74 + lo g_{10} (\frac{2.2245}{3.4255})

- 3 lo g_{2} (t) - lo g_{2} (3)

- 1 ln (\frac{s ^{2} - a ^{2}}{s ^{2}})

What is expand log_{d}((sqrt(a)b^5)/(c^7)) ?
The solution to expand log_{d}((sqrt(a)b^5)/(c^7)) is log_{d}(sqrt(a))+5log_{d}(b)-7log_{d}(c)