What is 1/2 (-5log_{10}(x)+log_{10}(yz^3)) ?

The solution to 1/2 (-5log_{10}(x)+log_{10}(yz^3)) is 1/2 log_{10}((yz^3)/(x^5))

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simplify 1/2 (-5log_{10}(x)+log_{10}(yz^3))

simplify

\frac{1}{2} (- 5 lo g_{10} (x) + lo g_{10} (y z^{3}))

\frac{1}{2} lo g_{10} (\frac{y z ^{3}}{x ^{5}})

Solution steps

\frac{1}{2} (- 5 lo g_{10} (x) + lo g_{10} (y z^{3}))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 lo g_{10} (x) = lo g_{10} (x^{5})

= \frac{1}{2} (- lo g_{10} (x^{5}) + lo g_{10} (y z^{3}))

Apply log rule:

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

lo g_{10} (y z^{3}) - lo g_{10} (x^{5}) = lo g_{10} (\frac{y z ^{3}}{x ^{5}})

= \frac{1}{2} (lo g_{10} (\frac{y z ^{3}}{x ^{5}}))

Remove parentheses:

(a) = a

= \frac{1}{2} lo g_{10} (\frac{y z ^{3}}{x ^{5}})

\frac{ln ( \frac{1034}{40353607} )}{2 ln ( 7 )}

lo g_{a} (5 x)

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

lo g_{10} (\frac{a ^{2}}{x})

ln (x^{11})

What is 1/2 (-5log_{10}(x)+log_{10}(yz^3)) ?
The solution to 1/2 (-5log_{10}(x)+log_{10}(yz^3)) is 1/2 log_{10}((yz^3)/(x^5))