The idiom describing water flow, please 3Q

The idiom describing water flow, please 3Q

The water is gurgling, the water is turbulent, the torrent bravely enters the big waves and washes sand for thousands of miles, the rough waves are rushing and flying, the flow is straight down, the water is clear to the bottom, the trickle is sparkling, and the blue waves are rippling

It is proved by comprehensive method that when 0

Find the proof idea with the analysis method and write the proof with the comprehensive method. The details are as follows
When 0

According to the algorithm of power, the n-th power of a is multiplied by the m-th power of a = the M + n-th power of a, and it is proved that log (MN) = logm + logn

Suppose the base is a
Then a ^ [log (a) (MN)] = Mn
a^[log(a)m+log(a)n]
=a^log(a)m*a^log(a)n
=mn
So log (MN) = logm + logn

Log basic formula log (a) (m ^ n) = NLog (a) (m) Push from left to right. Push from right to left

Log (a) m ^ n = log (a) m * m * m *... * m = log (a) m + log (a) m +... + log (a) M = NLog (a) m ellipsis has n

Hello, teachers. Let me ask you a math question; A problem of logarithmic base changing formula; log(a) （m^n)=nlog(a)(m). Log (a) (m ^ n) in language is; the logarithm of base a (m ^ n)! How to describe this NLog (a) (m) in language? Yes; n times the logarithm of base a m? Please help the teachers

This can be said to be the logarithm of N times a as the base m, or N times the logarithm of a as the base M

Logarithmic bottoming formula; log(a) (m^n)=nlog(a) (m). Log (a) (m ^ n) is described in language; Logarithm of base a (m ^ n)! How can this NLog (a) (m) be described in language? Yes; N times the logarithm of M Based on a? It's really difficult for me. Please help me

Well, it seems right! Are there any questions?