What is expand (1/2)log_{b}(a)-5log_{b}(c) ?

The solution to expand (1/2)log_{b}(a)-5log_{b}(c) is log_{b}((a^{1/2})/(c^5))

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expand (1/2)log_{b}(a)-5log_{b}(c)

expand

(\frac{1}{2}) lo g_{b} (a) - 5 lo g_{b} (c)

lo g_{b} (\frac{a ^{\frac{1}{2}}}{c ^{5}})

Solution steps

(\frac{1}{2}) lo g_{b} (a) - 5 lo g_{b} (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

(\frac{1}{2}) lo g_{b} (a) = lo g_{b} (a^{(\frac{1}{2})})

= lo g_{b} (a^{(\frac{1}{2})}) - 5 lo g_{b} (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{b} (a^{(\frac{1}{2})}) - lo g_{b} (c^{5})

Apply log rule:

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

lo g_{b} (a^{(\frac{1}{2})}) - lo g_{b} (c^{5}) = lo g_{b} (\frac{a ^{\frac{1}{2}}}{c ^{5}})

= lo g_{b} (\frac{a ^{\frac{1}{2}}}{c ^{5}})

Remove parentheses:

(a) = a

= lo g_{b} (\frac{a ^{\frac{1}{2}}}{c ^{5}})

ln (\frac{100 + 0.11}{0.11})

ln (\frac{0.5}{1.6})

\frac{1}{3} ln (\frac{49}{76})

- lo g_{10} (2.65 \cdot 1 0^{- 8})

1.76776 ln (\frac{1}{( 2 2 )}) + 0.61871

What is expand (1/2)log_{b}(a)-5log_{b}(c) ?
The solution to expand (1/2)log_{b}(a)-5log_{b}(c) is log_{b}((a^{1/2})/(c^5))