Question

given that log 2 =0.3010,log 3 =0.4771 and log 7=0.8451 then,find [1] log37.5 and [2] log 12.25

Answer 1

I'll show you how to do the first one and you should then be able to use the same techniques to solve the second one.\[\log37.5=\log\frac{75}{2}=\log\frac{3*25}{2}=\log\frac{3*5^2}{2}\]\[\qquad=\log3+\log5^2-\log2\]\[\qquad=\log3+2\log5-\log2\]\[\qquad=\log3+2\log\frac{10}{2}-\log2\]\[\qquad=\log3+2(\log10-\log2)-\log2\]\[\qquad=\log3+2(1-\log2)-\log2\]\[\qquad=\log3+2-2\log2-\log2\]\[\qquad=\log3+2-3\log2\]\[\qquad=0.4771+2-3*0.3010\]\[\qquad=1.5741\]