Prove that loga ^ m b ^ n = n / mloga B

Prove that loga ^ m b ^ n = n / mloga B

loga^m b^n=lgb^n/lga^m
=(n/m)*(lgb/lga)
=(n/m)*loga b

It is known that m, n ∈ n *, loga (m) + loga (1 + 1 / M) + loga (1 + 1 / M + 1) + +loga(1+1/m+n-1)=loga(m)+
It is known that m, n ∈ n *, a > 0, a ≠ 1, and loga (m) + loga (1 + 1 / M) + loga (1 + 1 / (M + 1)) + +Loga (1 + 1 / (M + n-1)) = loga (m) + loga (n), find the value of M, n. (a is the base)

loga(m)+loga(1+1/m)+loga(1+1/（m+1）)+…… +loga(1+1/(m+n-1))
=loga(m+n)
=loga(m)+loga(n)
=loga(mn)
m+n=mn
1/m+1/n=1,m,n∈N*,
So: M = n = 2

Why is the n-th power of a logam equal to N times the logam

logax+logay=loga(xy)
The n-th power of a logam is the sum of n logams

Given that a B belongs to R +, and m n belongs to N, then the M + n power + BM + n power of a and the m power of a, the n power of B + the n power of a, the m power of B?

A ^ (M + n) is defined as the M + n power of a, which is used as the difference method. When a ^ (M + n) + B ^ (M + n) - (a ^ m * B ^ n + A ^ n * B ^ m) = a ^ m (a ^ N-B ^ n) + B ^ m (b ^ n-a ^ n) = (a ^ M-B ^ m) (a ^ N-B ^ n) a = B, the two are obviously equal. When a ≠ B, because m n belongs to N, y = x ^ m, y = x ^ n all belong to increasing function, a ^ m > b ^ m, a ^ n > b ^ Na

Logamn = logam Logan. Right
thank you

No, it should be plus. If the front is m / N, the back is minus

Why do the great gods help

You can set X = logam, y = Logan, z = logamn... To get that the x power of a is equal to M. then you should know how to solve it

logaM+logaN=

logaM+logaN=loga MN

Proving logam / N = logam Logan

Let a ＾ x = m, a ＾ y = n
M/N=(a＾x)/(a＾y)=a＾(x-y)
loga (M/N)=loga a＾(x-y)=x-y
loga M-loga N=x-y
So log a (M / N) = log a m-log a n

Given a + B = C, A-B = D, prove that a = B is equivalent to C ⊥ D, and explain its geometric meaning. (a, B, C, D are vectors)

The quantitative products of vectors are: a + B = C; A-B = D = = > (a + b) * (a-b) = C * d = = > | a | & # 178; - | B | & # 178; = C * D | a | = | B | a | & # 178; - | B | & # 178; = C * d = 0, C ⊥ D geometric meaning: in a parallelogram with vectors a and B as adjacent edges; A-B; and a + B represent plane respectively

The properties of logarithm

1) The logarithm of 1 equals 0
2) The logarithm of the base is equal to 1
3) The logarithm of the product is equal to the sum of the logarithms
4) The logarithm of the quotient is the difference between the logarithm of the divisor and the logarithm of the divisor
5) The logarithm of a power is the product of the power exponent and the logarithm of the base
6) Logarithmic identity
7) Bottom changing formula