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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

\frac{1}{2} lo g_{10} (b) = lo g_{10} (b^{\frac{1}{2}})

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

ln (2 y)

lo g_{2} (x y)

5 lo g_{7} (2 x) - \frac{1}{3} lo g_{7} (5 x + 1)

lo g_{10} (y) + 8 lo g_{10} (z)

- lo g_{10} (\frac{a}{b})

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