What is 1/2 log_{10}(c)+7log_{10}(d) ?

The solution to 1/2 log_{10}(c)+7log_{10}(d) is log_{10}(c^{1/2}d^7)

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simplify 1/2 log_{10}(c)+7log_{10}(d)

simplify

\frac{1}{2} lo g_{10} (c) + 7 lo g_{10} (d)

lo g_{10} (c^{\frac{1}{2}} d^{7})

Solution steps

\frac{1}{2} lo g_{10} (c) + 7 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}}) + 7 lo g_{10} (d)

Apply log rule:

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

7 lo g_{10} (d) = lo g_{10} (d^{7})

= lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{7})

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^{7}) = lo g_{10} (d^{7} c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}} d^{7})

\frac{1}{3} lo g_{k} (x) + 6 lo g_{k} (y) - 4 lo g_{k} (x)

lo g_{4} (8 x)

lo g_{3} (\frac{9}{y})

\frac{1}{2} lo g_{10} (a) + 4 lo g_{10} (b)

lo g_{7} (x) - lo g_{7} (x^{5})

What is 1/2 log_{10}(c)+7log_{10}(d) ?
The solution to 1/2 log_{10}(c)+7log_{10}(d) is log_{10}(c^{1/2}d^7)