What is log_{2}(((32x^{64}))/(128)) ?

The solution to log_{2}(((32x^{64}))/(128)) is 64log_{2}(x)-2

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simplify log_{2}(((32x^{64}))/(128))

simplify

lo g_{2} (\frac{( 32 x ^{64} )}{128})

64 lo g_{2} (x) - 2

Solution steps

lo g_{2} (\frac{32 x ^{64}}{128})

Factor the number:

128 = 32 \cdot 4

= lo g_{2} (\frac{32 x ^{64}}{32 \cdot 4})

Cancel the common factor:

32

= lo g_{2} (\frac{x ^{64}}{4})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{x ^{64}}{4}) = lo g_{2} (x^{64}) - lo g_{2} (4)

= lo g_{2} (x^{64}) - lo g_{2} (4)

lo g_{2} (x^{64}) = 64 lo g_{2} (x)

lo g_{2} (4) = 2

= 64 lo g_{2} (x) - 2

ln (x) - \frac{1}{2} (3 ln (x) + 5 ln (y))

3 ln (4) - 4 ln (3)

ln (x) - [ln (x + 1) + ln (x - 1)]

lo g_{b} (x) + lo g_{b} (y) - lo g_{b} (u)

\frac{1}{2} lo g_{b} (x) + 5 lo g_{b} (y) - 4 lo g_{b} (x)

What is log_{2}(((32x^{64}))/(128)) ?
The solution to log_{2}(((32x^{64}))/(128)) is 64log_{2}(x)-2