What is 1/2 log_{10}(c)+9log_{10}(d) ?

The solution to 1/2 log_{10}(c)+9log_{10}(d) is log_{10}(c^{1/2}d^9)

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simplify 1/2 log_{10}(c)+9log_{10}(d)

simplify

\frac{1}{2} lo g_{10} (c) + 9 lo g_{10} (d)

lo g_{10} (c^{\frac{1}{2}} d^{9})

Solution steps

\frac{1}{2} lo g_{10} (c) + 9 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}}) + 9 lo g_{10} (d)

Apply log rule:

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

9 lo g_{10} (d) = lo g_{10} (d^{9})

= lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{9})

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^{9}) = lo g_{10} (d^{9} c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}} d^{9})

lo g_{10} (6) + lo g_{10} (9)

ln (e^{3 x}) + ln (x^{3}) - ln (3 x)

ln (\frac{1}{1 + 1})

lo g_{4} (16 x)

ln (5) + 2 ln (x) - 11 ln (x^{2} + 5)

What is 1/2 log_{10}(c)+9log_{10}(d) ?
The solution to 1/2 log_{10}(c)+9log_{10}(d) is log_{10}(c^{1/2}d^9)