# logarithmic & exponential espressions

• Apr 27th 2009, 05:36 AM
b_austintx
logarithmic & exponential espressions
need help with 2 questions.

e^(3s) = r

would it be 3s = r ? would i take the log of each side? since it equals (r) and not a number i can't get (s) byself?

i just did log7t = g
and what i did with that one was 7t =10g but since there is not base or exponent?? not sure if that is the right answer.
since there is no exponet would it be zero? how can i log both sides?

then i divided the 10/7 getting (t) by itself. which gave me 1/7 = t ??
can anyone help??
• Apr 27th 2009, 06:03 AM
mr fantastic
Quote:

Originally Posted by b_austintx
need help with 2 questions.

e^(3s) = r Mr F says: Therefore 3s = ln (r). What you have below is wrong.

would it be 3s = r ? would i take the log of each side? since it equals (r) and not a number i can't get (s) byself?

i just did log7t = g Mr F says: Therefore 7t = 10^g. What you have below is wrong.

and what i did with that one was 7t =10g but since there is not base or exponent?? not sure if that is the right answer.
since there is no exponet would it be zero? how can i log both sides?

then i divided the 10/7 getting (t) by itself. which gave me 1/7 = t ??
can anyone help??

..
• Apr 27th 2009, 06:10 AM
b_austintx
so once i have 3s = r there is not much else i can do?? same with the
7t =10^g ??

i can't plug it in to my calculator log 10 ^g ?
• Apr 27th 2009, 07:05 AM
e^(i*pi)
Quote:

Originally Posted by b_austintx
so once i have 3s = r there is not much else i can do?? same with the
7t =10^g ??

i can't plug it in to my calculator log 10 ^g ?

As Mr F said: 3s = ln(r).

You can divide by 3 to make s the subject: $\displaystyle s = \frac{1}{3}ln(r)$

log(10^g) = g. I'm not sure what you mean there but there should be a "ten to the power of.." button on your calculator. It would be around inverse log.

log7t = g is ambiguous: do you mean log_7t = g or log_10(7t) = g.

If it's the former than t = 7^g but if it is the latter you get Mr F's answer of 7t = 10^g
• Apr 27th 2009, 07:38 AM
b_austintx
its just
log 7t = g

there is no base or exponent. its not ^ 7t. since there isn't an exponent or base i am confused. if there was an exponent, i would just move the exponent in front of log.

i can't log 10 ^g i can't raise g since there isn't a (g) button ??
• Apr 27th 2009, 07:43 AM
e^(i*pi)
Quote:

Originally Posted by b_austintx
its just
log 7t = g

there is no base or exponent. its not ^ 7t. since there isn't an exponent or base i am confused. if there was an exponent, i would just move the exponent in front of log.

i can't log 10 ^g i can't raise g since there isn't a (g) button ??

log without a base is usually base 10. Since you don't know g you have to leave it as 10^g rather than evaluate it - your equation has two unknowns so it can't be solved as it's written
• Apr 27th 2009, 08:07 AM
b_austintx
so my final answer is gonna be
7t =10 ^g

then 10^g * 7t ???
that doesnt make sense. or should i just leave it they way it is above?

because i'm not solving for t? right?
• Apr 27th 2009, 08:12 AM
e^(i*pi)
Quote:

Originally Posted by b_austintx
so my final answer is gonna be
7t =10 ^g

then 10^g * 7t ???
that doesnt make sense. or should i just leave it they way it is above?

because i'm not solving for t? right?

If you want to solve for t then divide by 7:

$\displaystyle t = \frac{1}{7} 10^g$
• Apr 27th 2009, 08:24 AM
b_austintx
that is my question. am i solving for (t) ??

the orignal problem is log 7t =g

so is that what i'm doing? cause then that would make sense to have it
t = 1/7 10 ^g

but i'm not sure if thats what i'm doing?? or would i just leave it as

7t =10^g ???

all its asking me to do is convert the equivlent logarithmic or exponential expression. so i don't think i'm solving it. right ??? i'm just being asked to convert.

what do you think?
• Apr 27th 2009, 01:21 PM
mr fantastic
Quote:

Originally Posted by b_austintx
that is my question. am i solving for (t) ??

the orignal problem is log 7t =g

so is that what i'm doing? cause then that would make sense to have it
t = 1/7 10 ^g

but i'm not sure if thats what i'm doing?? or would i just leave it as

7t =10^g ???

all its asking me to do is convert the equivlent logarithmic or exponential expression. so i don't think i'm solving it. right ??? i'm just being asked to convert.

what do you think?

You should post the original question, exactly as it's worded in your textbook or wherever you got it from.