Question

PLEASE HELP
1. 3^5x = 42

Answer 1

so is the question

\[3^{5x} = 42\]

Answer 2

yes :)

Answer 3

ok...

so the easiest thing to do is

Answer 4

take the log of both sides.... does that make sense..?

Answer 5

that what my teacher tried to teach me but i don't understand how :/

Answer 6

ok... so the log law you need to know about is the one that deals with powers
base


\[\log(a^b) = b \times \log(a)\]

so the log of a number involving a power can be written as the power times the log of the

Answer 7

so you would have

\[\log(3^{5x}) = \log(42)\]

any ideas on how to rewrite the left hand side..?

Answer 8

5x log 3 ?

Answer 9

great so you have

\[5x \times \log(3) = \log(42

log(3) and log(42) are just numbers...dividing both sides by log(3)

and that will give you a value for 5x,

then you can some for x.

you make want to check to question to see if you need a decimal approximation or an exact value

Answer 10

oops should read

\[5x \times \log(3) = \log(42)\]

and it doesn't matter which type of logs you use... base e or base 10

you'll get the same answer

Answer 11

I'd expect the value of x is between .6 and .8.... probably around 0.7

Answer 12

so i divide in my calculator log 3/log 42

Answer 13

oh no wait its the other way around

Answer 14

no other way

\[5x = \frac{\log(42)}{\log(3)}\]

then divide the answer by 5

Answer 15

and then i divided that by 5 and the answer i got was 0.6804...

Answer 16

makes sense to me

yo check you can use

\[3^{5 \times 0.6804}\

and see if you get 42

Answer 17

yes its right. thank you for your help. mind helping with a few more?

Answer 18

well post them as new questions and if I'm still here I'll look at them. There are lots of people her who provide great help