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

The solution to expand log_{8}((w^4x^2)/(yz)) is 4log_{8}(w)+2log_{8}(x)-log_{8}(y)-log_{8}(z)

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

expand

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

4 lo g_{8} (w) + 2 lo g_{8} (x) - lo g_{8} (y) - lo g_{8} (z)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{8} (w^{4} x^{2}) = lo g_{8} (w^{4}) + lo g_{8} (x^{2}), lo g_{8} (yz) = lo g_{8} (y) + lo g_{8} (z)

= lo g_{8} (w^{4}) + lo g_{8} (x^{2}) - (lo g_{8} (y) + lo g_{8} (z))

Apply log rule:

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

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

= 4 lo g_{8} (w) + lo g_{8} (x^{2}) - (lo g_{8} (y) + lo g_{8} (z))

Apply log rule:

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

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

= 4 lo g_{8} (w) + 2 lo g_{8} (x) - (lo g_{8} (y) + lo g_{8} (z))

- (lo g_{8} (y) + lo g_{8} (z)) : - lo g_{8} (y) - lo g_{8} (z)

= 4 lo g_{8} (w) + 2 lo g_{8} (x) - lo g_{8} (y) - lo g_{8} (z)

lo g_{10} (512) - lo g_{10} (366)

lo g_{10} (rs) - 3 lo g_{10} (p) + 7

ln (2) + ln (3)

5 ln (x) + ln (x + 1)

What is expand log_{8}((w^4x^2)/(yz)) ?
The solution to expand log_{8}((w^4x^2)/(yz)) is 4log_{8}(w)+2log_{8}(x)-log_{8}(y)-log_{8}(z)