What is expand log_{2}((8x^4)/5) ?

The solution to expand log_{2}((8x^4)/5) is 3+4log_{2}(x)-log_{2}(5)

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expand log_{2}((8x^4)/5)

expand

lo g_{2} (\frac{8 x ^{4}}{5})

3 + 4 lo g_{2} (x) - lo g_{2} (5)

Solution steps

lo g_{2} (\frac{8 x ^{4}}{5})

Apply log rule:

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

lo g_{2} (\frac{8 x ^{4}}{5}) = lo g_{2} (8 x^{4}) - lo g_{2} (5)

= lo g_{2} (8 x^{4}) - lo g_{2} (5)

Apply log rule:

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

lo g_{2} (8 x^{4}) = lo g_{2} (8) + lo g_{2} (x^{4})

= lo g_{2} (8) + lo g_{2} (x^{4}) - lo g_{2} (5)

Apply log rule:

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

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

= lo g_{2} (8) + 4 lo g_{2} (x) - lo g_{2} (5)

lo g_{2} (8) = 3

= 3 + 4 lo g_{2} (x) - lo g_{2} (5)

4 ln (x) + 2 ln (y) - 6 ln (z)

(85) lo g_{\frac{1}{2}} (\frac{90}{100})

lo g_{6} (\frac{3 x}{36 y ^{4}})

lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (x + 3)

ln (x + 2) + ln (x - 2)

What is expand log_{2}((8x^4)/5) ?
The solution to expand log_{2}((8x^4)/5) is 3+4log_{2}(x)-log_{2}(5)