Question

Angie was working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation and how solving would be different if the bases were equal.

Answer 1

23^x my bad

Answer 2

To solve an exponential equation take logarithms of both sides.
Can you do that?

Answer 3

could you give me an example? I think I know what you are talking about. c:

Answer 4

okay a good example is
solve for x

23^x = 6
log (23^x) = log 6
x * log (23) = log(6)

Answer 5

you would have to take the natural log of both sides and move the exponent down using the logarithmic laws (i.e. xlog23 = log6).

Answer 6

MathMusician - you do not have to take natural logs of both sides.
You can use base 10 logs or logs of any base.

Answer 7

So I do that and solve it?

Answer 8

x * log (23) = log(6) solve this I mean?

Answer 9

Well do you know how to calculate logs?
A lot of calculators can.
If not here's an online log calculator
www.1728.org/logrithm.htm

Answer 10

is there a base for this or no?

Answer 11

Clickable link:
http://www.1728.org/logrithm.htm

Answer 12

wait would I make 10 the base?

Answer 13

You can use any base but I like using base 10 as opposed to natural logs

Answer 14

Okay I am gonna show you what I have and tell me if I did this right .

Answer 15

x*log10(23)=log10(6)
divide both sides by log10(23)
x=log10(6)/log10(23)
(decimal x=0.57144)

Answer 16

x * 1.361727836 = 0.77815125038
x = 0.77815125038 / 1.361727836
x = 0.5714440359

I'd say you did that correctly !!

Answer 17

so would I put
x*log10(23)=log10(6)
divide both sides by log10(23)
x=log10(6)/log10(23)
(decimal x=0.57144)
as my answer?

Answer 18

Yes, although I don't think you'd have to say decimal x = .57144
The answer is not a logarithm
it is a regular number in base 10

Answer 19

Okay thank you c: I have two more questions I am gonna post will you look at them?

Answer 20

well okay go ahead