What is 34log_{2}(a)-13log_{2}(b)+5log_{2}(c) ?

The solution to 34log_{2}(a)-13log_{2}(b)+5log_{2}(c) is log_{2}((a^{34}c^5)/(b^{13)})

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simplify 34log_{2}(a)-13log_{2}(b)+5log_{2}(c)

simplify

34 lo g_{2} (a) - 13 lo g_{2} (b) + 5 lo g_{2} (c)

lo g_{2} (\frac{a ^{34} c ^{5}}{b ^{13}})

Solution steps

34 lo g_{2} (a) - 13 lo g_{2} (b) + 5 lo g_{2} (c)

Apply log rule:

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

34 lo g_{2} (a) = lo g_{2} (a^{34})

= lo g_{2} (a^{34}) - 13 lo g_{2} (b) + 5 lo g_{2} (c)

Apply log rule:

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

13 lo g_{2} (b) = lo g_{2} (b^{13})

= lo g_{2} (a^{34}) - lo g_{2} (b^{13}) + 5 lo g_{2} (c)

Apply log rule:

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

lo g_{2} (a^{34}) - lo g_{2} (b^{13}) = lo g_{2} (\frac{a ^{34}}{b ^{13}})

= lo g_{2} (\frac{a ^{34}}{b ^{13}}) + 5 lo g_{2} (c)

Apply log rule:

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

5 lo g_{2} (c) = lo g_{2} (c^{5})

= lo g_{2} (\frac{a ^{34}}{b ^{13}}) + lo g_{2} (c^{5})

Apply log rule:

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

lo g_{2} (\frac{a ^{34}}{b ^{13}}) + lo g_{2} (c^{5}) = lo g_{2} (\frac{a ^{34}}{b ^{13}} c^{5})

= lo g_{2} (\frac{a ^{34}}{b ^{13}} c^{5})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{2} (\frac{a ^{34} c ^{5}}{b ^{13}})

ln (3 \cdot 1 0^{14})

lo g_{5} (\frac{25}{x + 4})

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

5 lo g_{10} (x) + 4 lo g_{10} (x - 9)

lo g_{5} (8) - lo g_{5} (x)

What is 34log_{2}(a)-13log_{2}(b)+5log_{2}(c) ?
The solution to 34log_{2}(a)-13log_{2}(b)+5log_{2}(c) is log_{2}((a^{34}c^5)/(b^{13)})