What is 1/2 log_{10}(c)+5log_{10}(d) ?

The solution to 1/2 log_{10}(c)+5log_{10}(d) is log_{10}(c^{1/2}d^5)

Popular >

simplify 1/2 log_{10}(c)+5log_{10}(d)

simplify

\frac{1}{2} lo g_{10} (c) + 5 lo g_{10} (d)

lo g_{10} (c^{\frac{1}{2}} d^{5})

Solution steps

\frac{1}{2} lo g_{10} (c) + 5 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}}) + 5 lo g_{10} (d)

Apply log rule:

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

5 lo g_{10} (d) = lo g_{10} (d^{5})

= lo g_{10} (c^{\frac{1}{2}}) + lo g_{10} (d^{5})

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^{5}) = lo g_{10} (d^{5} c^{\frac{1}{2}})

= lo g_{10} (c^{\frac{1}{2}} d^{5})

lo g_{6} (x^{4} y^{6})

4 ln (x) - \frac{1}{8} ln (y)

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{10} (\frac{x ^{2}}{2})

What is 1/2 log_{10}(c)+5log_{10}(d) ?
The solution to 1/2 log_{10}(c)+5log_{10}(d) is log_{10}(c^{1/2}d^5)