Question

solve 4+3^5x=8 for x.

Answer 1

Is it ?
\[4+3^{5 x}=8
\]
@andria_elizabeth

Answer 2

yes

Answer 3

Subtract 4 from both the sides, what would you get?

Answer 4

3 ^5x=4

Answer 5

Do you know logarithms?

Answer 6

a little bit but thats what im confused on, can you please help me out?

Answer 7

Yeah, Let's take log both the sides, base is 10
\[\log 3^{5x}=\log 4\]
Now log has a property
\[\log a^b=b\log a\]
Let's use this here
\[\log 3^{5x} =\log 4\]
\[ 5x \log 3= \log 4\]
Do you get this?

Answer 8

why is it log 4?

Answer 9

is it proabably good for me to memorize the properties?

Answer 10

You have 4 on the right side, we applied log to both the sides. That's how we get
\[5x\times \log 3=\log 4\]
Yeah, you should memorize all logarithmic properties.

Answer 11

@andria_elizabeth Now we should refer the log tables, to find the value of log 4 and log 3.
Both are to base 10

Answer 12

okay so even if it didnt have log before we still put it? and how do we find the value tho?

Answer 13

Let's see the definition of log
\[\log_b a =c\]
\[=> a=b^c\]
So if you have
\[\log_{10} 100=2\]
This implies
\[100=10^2\]
which is true. Do you get it?
We could have any base bu it should be >0 and not equal to 1

Answer 14

yeah, i understand that part

Answer 15

so here we have log to base 10
If you refer log tables or use calulator
\[\log 3=0.477\]
\[\log 4=0.6020\]
Now we have
\[3x\times 0.477=0.602\]
Can you find x from here?

Answer 16

i just take .477 away from .602?

Answer 17

Nope, you have to divide 0.602 by 0.477

Answer 18

why is that?

Answer 19

\[3x=\frac{0.602}{0.477}\]

Answer 20

once we divide that then we divide again by 3x?

Answer 21

yes. Just 3 you need to find x

Answer 22

oh okay, thanks

Answer 23

Welcome :)

Answer 24

:]