What is log_{8}(c)+4log_{8}(a)-5log_{8}(b) ?

The solution to log_{8}(c)+4log_{8}(a)-5log_{8}(b) is log_{8}((ca^4)/(b^5))

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simplify log_{8}(c)+4log_{8}(a)-5log_{8}(b)

simplify

lo g_{8} (c) + 4 lo g_{8} (a) - 5 lo g_{8} (b)

lo g_{8} (\frac{c a ^{4}}{b ^{5}})

Solution steps

lo g_{8} (c) + 4 lo g_{8} (a) - 5 lo g_{8} (b)

Apply log rule:

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

4 lo g_{8} (a) = lo g_{8} (a^{4})

= lo g_{8} (c) + lo g_{8} (a^{4}) - 5 lo g_{8} (b)

Apply log rule:

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

lo g_{8} (c) + lo g_{8} (a^{4}) = lo g_{8} (c a^{4})

= lo g_{8} (c a^{4}) - 5 lo g_{8} (b)

Apply log rule:

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

5 lo g_{8} (b) = lo g_{8} (b^{5})

= lo g_{8} (c a^{4}) - lo g_{8} (b^{5})

Apply log rule:

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

lo g_{8} (c a^{4}) - lo g_{8} (b^{5}) = lo g_{8} (\frac{c a ^{4}}{b ^{5}})

= lo g_{8} (\frac{c a ^{4}}{b ^{5}})

lo g_{4} (7^{2} 3^{4})

ln (2 x y)

lo g_{2} (x + 1) - lo g_{2} (2 - x)

lo g_{2} (3 x^{4})

3 ln (x) - \frac{1}{3} ln (y)

What is log_{8}(c)+4log_{8}(a)-5log_{8}(b) ?
The solution to log_{8}(c)+4log_{8}(a)-5log_{8}(b) is log_{8}((ca^4)/(b^5))