Exponential and logarithmic functions Questions!

[vexx]

Hi,

Can anyone help explain these few questions (all from the same exercise that i cannot do .__.)

1. Solve for X
3^(2x)−3^(x+2)+8=0

2.
Prove that logb^a + logc^b + loga^c= 1/(loga^b) + 1/(logb^c) + 1/(logc^a)
(logb^a= log base of b, to the power of a), sorry for not using tex

3.
Prove that if (logr^p =q) and (logq^r=p), then (logq^p=pq)

4.
Solve the equation log5^x = 16 logx^5

Sorry there's a few!

Thanksss

Vexx

[m@tty]

1.





let





or

But

So
or

or .

[physics]

I GOT number 1

let 3^x = a
so u would get a^2 - 9a +8 =0
which then goes to (a-8) (a-1) =0
and then a=8 and a= 1
which then goes back to
3^x= 8   and 3^x=1
whcih is log (little 3) 8 =x  and x=1
oh yeh i solved it finally i'm useful on here

[physics]

1.





let





or

But

So
or

or .

damn i was too slow =.=

[m@tty]

2.
Prove

The change of base rule states that

Using this rule here and making the base of both logarithms in the fraction be equal to the value being logarithm'd (I've forgotten what it is called officially.... but the in the above example).



Simplifying this using the fact that



QED.

[m@tty]

3.

If and , then prove that



Now from the previous question it was proved that

So,

Therefore,

And using the facts given above

QED

Nice questions

[Aqualim]

4.

[the.watchman]

4.









OR

[vexx]

Thank you so much all, such quick answers^^;

Aqualim- sorry to be a noob, but we've never learnt anything about those "In" symbols, i see them sometimes on the calc. and have no idea what they mean, do they correspond to a certain log or something?

One more question sorry:
Given that q^p = 25, find log5^q in terms of p.

[superflya]

ln= log to base e.

[the.watchman]

ln = natural log =

[vexx]

thank youu! i get it now..

[Mao]

@Aqualim - Natural logarithm is typically represented as ln with a L, not I.

ln is often used to distinguish log_e from log₁₀ for introductory level maths and empirical sciences (since log₁₀ is used quite extensively, it is often abbreviated to log with no subscript). When moving on to the heavy-duty maths and theoretical sciences, the subscript is again dropped, but referring to base e (the only log used at this level is with base e. In fact in pretty much all computational packages, the function Log refers to Log_e).

[QuantumJG]

@Aqualim - Natural logarithm is typically represented as ln with a L, not I.

With the maths being VCE level, I would only use , because log by itself could cost you methods marks.

Once you leave high school maths, the only useful parts of log and some exponenential is or , because of what you can do with these. 

[the.watchman]

@Aqualim - Natural logarithm is typically represented as ln with a L, not I.

With the maths being VCE level, I would only use , because log by itself could cost you methods marks.

Once you leave high school maths, the only useful parts of log and some exponenential is or , because of what you can do with these. 

Yeah, I agree
It's probably best to avoid using 'ln' in your working and write instead
This is the 'proper' way to write it