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

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

yes

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

3 ^5x=4

Do you know logarithms?

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

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?

why is it log 4?

is it proabably good for me to memorize the properties?

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.

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

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

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

yeah, i understand that part

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?

i just take .477 away from .602?

Nope, you have to divide 0.602 by 0.477

why is that?

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

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

yes. Just 3 you need to find x

oh okay, thanks

Welcome :)

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