Question

Can someone please explain how to solve a log equation with an example.

Answer 1

how 'bout u pick an example....

Answer 2

otherwise i'll choose the easiest...:)

Answer 3

OK ...
\[5^{x - 3} . 3^{2x-8} = 225\]

Answer 4

How to solve this using log?
I'm new so I have no idea.

Answer 5

I mean new to log.

Answer 6

pls help.

Answer 7

welcome to logarithms!

Answer 8

Yeah thanks!

Answer 9

I guess you can solve this without using Logs..

Answer 10

But I want to know how to do it with log.

Answer 11

Okay then all here will explain you how to do this...

Answer 12

15^(x-3)+(2x-8)=225
now we take ln
(3x-11)15= ln225

Answer 13

What is In?
And how did you get 15^(x-3)+(2x-8)=225?

Answer 14

15*ln(3x-11)=ln 225

Answer 15

by multi 3 into 5 to get 15
and the exponent it's added

Answer 16

But how can you just multiply the base and add the exponents?

Answer 17

Use the following formulas of Logs:

\[\large Log(a \times b) = Log(a) + Log(b)\]

\[\large Log(a)^b = b.Log(a)\]

Answer 18

before we take the logarithem

Answer 19

it's from exponent experepties

Answer 20

Why did you delete that @dpaInc?

Answer 21

because i don't wanna take away from these guys awesome explanations....:)

Answer 22

See, take Log both the sides you will get:

\[\large Log(5^{x-3}.3^{2x-8}) = Log(225)\]

Now use the formulas I have written above..

Answer 23

Use the first formula only...

Answer 24

\[\log(5^{x-3}) . \log(3^{2x-8}) = \log 225 \]

Answer 25

Now Check my first formula carefully...

Answer 26

@pratu043 trust take my answer

Answer 27

like what waterineyes did now

Answer 28

That's what I've done here right @waterineyes?

Answer 29

I give you an example:

\[\large Log(2 \times 3) = Log(2) + Log(3)\]

Go by this procedure...

Answer 30

I've already done that. So now we should use the second one?

Answer 31

You have done it wrongly my friend...

Answer 32

See check the formula..
After formula the result will be in sum form and your result is not in sum form..
Is there any + sign in your result???

Answer 33

Oops.
\[\log(5^{x-3}) + \log(3^{2x-8}) = \log225\]

Answer 34

Yes now you are right...

Now 225 is square of what number???

Answer 35

15

Answer 36

So can you write 225 as \(15^2\) on right hand side.??

If yes then do it..

Answer 37

\[\log(5^{x-3}) + \log(3^{2x-8}) = \log15^{2}\]

Answer 38

Now use the power rule of Logarithms that is the Second Formula that I have given above..

Can you use that??

Answer 39

I give you an example of that too:

\[\large Log(x)^4 = 4.Log(x)\]

Answer 40

\[(x-3)\log5 + (2x-8)\log3 = 2\log15\]

Answer 41

Can you write 15 as 3*5??

Answer 42

Yes.
\[(x-3)\log5 + (2x-8)\log3 = 2\log(5 * 3)\]

Answer 43

Then use it and use the first formula again on right hand side...

Answer 44

\[(x-3)\log5 + (2x-8)\log3 = 2\log5 + 2\log3\]

Answer 45

Now what you have to do is to compare the coefficients of \(Log3\) and \(Log5\) both the sides can you do that??

Answer 46

Tell me the coefficient of Log3 on Left hand side and right hand side...

Answer 47

On LHS its 2x - 8 and on RHS its 2.

Answer 48

Just equate them and find x from it..

Answer 49

Similarly equate the coefficients of log5 and then also find x you will get the same x in both the case...

Answer 50

No no...

Answer 51

\[(2x-8)\log3 = 2\log3\]

Answer 52

I said to equate the coefficients buddy..

Coefficients are 2x - 8 and 2..
you should equate this only...

Answer 53

So you should just do 2x-8 = 2?

Answer 54

x = 5

Answer 55

See, if :

\[\large xlog3 = ylog3\]

implies x = y.

Getting??

Answer 56

Yes!!

Answer 57

Yes you have found x = 5 that is absolutely right...

Answer 58

Thanks a lot!!

Answer 59

Now equate the coefficients of log5..

Answer 60

x - 3 = 2
x = 2 + 3
= 5

Answer 61

Yes got the same value of x so you are right..

If anyhow x values are coming different then either question is wrong or your solution is wrong..

Getting??