If-log-2-3-a-and-log-3-7-b-express-log-42-56-in-terms-of-a-and-b-

Question Number 137764 by byaw last updated on 06/Apr/21

If \log_{2} 3 = a and \log_{3} 7 = b, express

\log_{42} 56 in terms of a and b

Answered by EnterUsername last updated on 06/Apr/21

{l o g}_{2} 3 = a, {l o g}_{3} 7 = \frac{{l o g}_{2} 7}{{l o g}_{2} 3} = b \Rightarrow {l o g}_{2} 7 = a b

{l o g}_{42} 56 = \frac{{l o g}_{2} 56}{{l o g}_{2} 42} = \frac{{l o g}_{2} (8 \times 7)}{{l o g}_{2} (6 \times 7)} = \frac{{l o g}_{2} 2^{3} + {l o g}_{2} 7}{{l o g}_{2} 2 + {l o g}_{2} 3 + {l o g}_{2} 7}

= \frac{3 + a b}{1 + a + a b}

Commented by otchereabdullai@gmail.com last updated on 08/Apr/21

wow!