SOLUTION: Hi, please could you give me a hand on these questions? I have tried hard but i can't find my way with proofs: 3i)Prove that log of m (in the base a)

SOLUTION: Hi, please could you give me a hand on these questions? I have tried hard but i can't find my way with proofs: 3i)Prove that log of m (in the base a) - log of n (in the base a)

Question 72121: Hi, please could you give me a hand on these questions? I have tried hard but i can't find my way with proofs:
3i)Prove that log of m (in the base a) - log of n (in the base a) = log of (m over n)( in the base a).
4i)Prove that nlog of x (in the base m) = log of x to the power of n (in the base m).
5a)Prove that log of b (in the base a) = log of b( in the base 10) over log of a (in the base 10).
Thank you very much for your help!!!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
let log(base a)m = X ; let log(base a)n= Y
Then a^(X)=m and a^Y=n
Then m/n = a^X/a^Y = a^(X-Y)
Take the log(base a) of both sides to get:
log(base a)(m/n) = log(base a)a^(X-Y)
log(base a)(m/n) = X-y
log(base a)(x/n) = log(base a)m - log(base a)n
==============
The proof for log(base a)mn = log(base a)m + log(base a)n
is almost identical:
You get a line that says:
mn=a^X * a^Y = a^(X+Y)
Take the log(base a) of both sides to get:
log(base a)mn = log(base a)a^(X+Y)
log(base a)mn = X+Y
log(base a)mn = log(base a)m + log(base a)n
-------------
log(base a)m^n = ?
Let log(base a)m = X
Then a^X = m
Substitute for "m" to get:
log(base a)(a^X)^n = log(base a)a^(Xn)= Xn
Substitute for X to get:
=nlog(base a)m
----------------
Log(base a)b = x
Let a^x = b
Then x log(base 10) a = log(base 10 b
And x= [log(base 10)b] / [log(base 10)a]
Substitute for "x" to get
log(base a)b = log(base 10)b /log(base 10)a
-----------
Cheers,
Stan H.

RELATED QUESTIONS
Hi >> I have a test after two weeks in this unit can you please give me hard questions... (answered by Edwin McCravy)

Hey :D i attemped this geometry based homework 2 weeks ago, i managed to do questions... (answered by scott8148)

I tried to listen in class, but the teacher was talking way over my head, and I lost her. (answered by Alan3354,solver91311)

i have a question. what the poop is going on with proofs its so hard and my teacher... (answered by lynnlo)

I have a grade 7 math quiz tomorrow can you give me some hard questions on surface area... (answered by MO dawg)

hi please can you help me with coterminal angles i try really hard in school but i... (answered by stanbon)

I do not understand how to solve these. I have tried to ask my teacher, but there are too (answered by stanbon)

I need to know how to write a polynomial equation of least degree with roots -3i, 3i, i, (answered by scott8148)

Hi, My name is Lauren and I really need help with my homework. Can you please help me... (answered by stanbon)