What is expand log_{10}((ysqrt(z))/(x^4)) ?

The solution to expand log_{10}((ysqrt(z))/(x^4)) is log_{10}(y)+log_{10}(sqrt(z))-4log_{10}(x)

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expand log_{10}((ysqrt(z))/(x^4))

expand

lo g_{10} (\frac{y z}{x ^{4}})

lo g_{10} (y) + lo g_{10} (z) - 4 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{y z}{x ^{4}})

Apply log rule:

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

lo g_{10} (\frac{y z}{x ^{4}}) = lo g_{10} (y z) - lo g_{10} (x^{4})

= lo g_{10} (y z) - lo g_{10} (x^{4})

Apply log rule:

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= lo g_{10} (y z) - 4 lo g_{10} (x)

Apply log rule:

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

lo g_{10} (y z) = lo g_{10} (y) + lo g_{10} (z)

= lo g_{10} (y) + lo g_{10} (z) - 4 lo g_{10} (x)

ln (\frac{21}{44})

lo g_{d} (\frac{a b ^{5}}{c ^{7}})

6.1 + lo g_{10} (\frac{15}{6.7})

ln (5) + 1 + ln (y) - ln (x)

4.74 + lo g_{10} (\frac{2.2245}{3.4255})

What is expand log_{10}((ysqrt(z))/(x^4)) ?
The solution to expand log_{10}((ysqrt(z))/(x^4)) is log_{10}(y)+log_{10}(sqrt(z))-4log_{10}(x)