Question

高一数学题 对数：log2^3=p log3^7=q log12^42=? 刚刚学对数还不太熟，

高一数学题 对数：log2^3=p log3^7=q log12^42=? 刚刚学对数还不太熟，希望过程详细点。谢谢！

Answer 1

解log12（42）
=lg42/lg12
=（lg2+lg3+lg7）/(lg2^2+lg3)
=（lg2+lg3+lg7）/(2lg2+lg3)
=（lg2/lg3+lg3/lg3+lg7/lg3）/(2lg2/lg3+1)
=（log3(2)+1+log3(7))/(2log3(2)+1)
=（1/log2(3)+1+log3(7))/(2/log2(3)+1)
=(1/p+1+q)/(2/p+1)
=(1+p+pq)/(2+p)

追问

我明白了，谢谢你啦！