What is 1/2 log_{10}(c)+3log_{10}(d) ?

The solution to 1/2 log_{10}(c)+3log_{10}(d) is log_{10}(c^{1/2}d^3)

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simplify 1/2 log_{10}(c)+3log_{10}(d)

simplify

\frac{1}{2} lo g_{10} (c) + 3 lo g_{10} (d)

lo g_{10} (c^{\frac{1}{2}} d^{3})

Solution steps

\frac{1}{2} lo g_{10} (c) + 3 lo g_{10} (d)

Apply log rule:

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

\frac{1}{2} lo g_{10} (c) = lo g_{10} (c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}}) + 3 lo g_{10} (d)

Apply log rule:

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

3 lo g_{10} (d) = lo g_{10} (d^{3})

= lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{3})

Apply log rule:

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

lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{3}) = lo g_{10} (d^{3} c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}} d^{3})

- \frac{5}{7} lo g_{2} (\frac{5}{7}) - \frac{2}{7} lo g_{2} (\frac{2}{7})

lo g_{10} (\frac{x ^{5}}{y ^{4}})

ln (\frac{x + 9}{x ( x - 4 )})

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

lo g_{10} (2) + lo g_{10} (9)

What is 1/2 log_{10}(c)+3log_{10}(d) ?
The solution to 1/2 log_{10}(c)+3log_{10}(d) is log_{10}(c^{1/2}d^3)