What is 1/2 log_{c}(+5log_{d}(x)) ?

The solution to 1/2 log_{c}(+5log_{d}(x)) is 1/2 log_{c}(5)+1/2 log_{c}(log_{d}(x))

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simplify 1/2 log_{c}(+5log_{d}(x))

simplify

\frac{1}{2} lo g_{c} (+ 5 lo g_{d} (x))

\frac{1}{2} lo g_{c} (5) + \frac{1}{2} lo g_{c} (lo g_{d} (x))

Solution steps

\frac{1}{2} lo g_{c} (5 lo g_{d} (x))

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{c} (5 lo g_{d} (x)) = lo g_{c} (5) + lo g_{c} (lo g_{d} (x))

= \frac{1}{2} (lo g_{c} (5) + lo g_{c} (lo g_{d} (x)))

Apply the distributive law:

a (b + c) = ab + a c

\frac{1}{2} (lo g_{c} (5) + lo g_{c} (lo g_{d} (x))) = \frac{1}{2} lo g_{c} (5) + \frac{1}{2} lo g_{c} (lo g_{d} (x))

= \frac{1}{2} lo g_{c} (5) + \frac{1}{2} lo g_{c} (lo g_{d} (x))

\frac{1}{4} [3 ln (x + 4) - ln (x) - ln (x^{2} - 25)]

- ln (x) + ln (x + 1)

lo g_{2} (x^{2} y^{3}) - lo g_{2} (x) - lo g_{2} (y)

3 lo g_{10} (x \cdot x^{3})

\frac{1}{2} lo g_{10} (16) - \frac{1}{3} lo g_{10} (8) + 1

What is 1/2 log_{c}(+5log_{d}(x)) ?
The solution to 1/2 log_{c}(+5log_{d}(x)) is 1/2 log_{c}(5)+1/2 log_{c}(log_{d}(x))