What is log_{2}((cd^3)/(e^4)) ?

The solution to log_{2}((cd^3)/(e^4)) is log_{2}(c)+3log_{2}(d)-4log_{2}(e)

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simplify log_{2}((cd^3)/(e^4))

simplify

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

lo g_{2} (c) + 3 lo g_{2} (d) - 4 lo g_{2} (e)

Solution steps

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

Apply log rule:

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

lo g_{2} (\frac{c d ^{3}}{e ^{4}}) = lo g_{2} (c d^{3}) - lo g_{2} (e^{4})

= lo g_{2} (c d^{3}) - lo g_{2} (e^{4})

Apply log rule:

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

lo g_{2} (e^{4}) = 4 lo g_{2} (e)

= lo g_{2} (c d^{3}) - 4 lo g_{2} (e)

Apply log rule:

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

lo g_{2} (c d^{3}) = lo g_{2} (c) + lo g_{2} (d^{3})

= lo g_{2} (c) + lo g_{2} (d^{3}) - 4 lo g_{2} (e)

Apply log rule:

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

lo g_{2} (d^{3}) = 3 lo g_{2} (d)

= lo g_{2} (c) + 3 lo g_{2} (d) - 4 lo g_{2} (e)

lo g_{10} (8^{2}) - lo g_{10} (12 5^{2})

lo g_{10} (3 (x + 1)^{2})

ln (x) - ln (x + 1)

9 ln (x) - \frac{1}{5} ln (y)

3 ln (x) - 2 ln (x - 1) + 1

What is log_{2}((cd^3)/(e^4)) ?
The solution to log_{2}((cd^3)/(e^4)) is log_{2}(c)+3log_{2}(d)-4log_{2}(e)