What is 1/2 log_{10}(c)+6log_{10}(d) ?

The solution to 1/2 log_{10}(c)+6log_{10}(d) is log_{10}(c^{1/2}d^6)

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simplify 1/2 log_{10}(c)+6log_{10}(d)

simplify

\frac{1}{2} lo g_{10} (c) + 6 lo g_{10} (d)

lo g_{10} (c^{\frac{1}{2}} d^{6})

Solution steps

\frac{1}{2} lo g_{10} (c) + 6 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}}) + 6 lo g_{10} (d)

Apply log rule:

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

6 lo g_{10} (d) = lo g_{10} (d^{6})

= lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{6})

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^{6}) = lo g_{10} (d^{6} c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}} d^{6})

lo g_{a} (\frac{1}{6})

lo g_{3} (\frac{9}{x + 5})

lo g_{a} (75) + lo g_{a} (2)

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

What is 1/2 log_{10}(c)+6log_{10}(d) ?
The solution to 1/2 log_{10}(c)+6log_{10}(d) is log_{10}(c^{1/2}d^6)