Question

Log equations help please?

Answer 1

What's the question? :)

Answer 2

It should be there?

Answer 3

Here it is

Answer 4

If this doesn't help, please come back: https://www.mathsisfun.com/algebra/logarithms.html :)

Answer 5

Still confused

Answer 6

The log laws:
\[1. \log_a(a)=1\]
\[2. \log_c(a^b)=blog_c(a)\]
\[3. \log_c(ab)=\log_c(a)+\log_c(b)\]

Answer 7

Okay so given:
\[7^x=213\]
Applying\[\log_7\]
to both sides, we get:
\[\log_7(7^x)=\log_7(213) \]
Then can you carry on, by applying the log laws I have just shown you above to rearrange the equation in terms of x?

Answer 8

Abut then the log_7 would cancel to make the same as we started with?

Answer 9

Hmmm, can you write it up and show me? Can you justify each step as well?

Answer 10

my internet when I posted this was awful; and I could not respond, so now I come back days later asking for help (with working internet).

Answer 11

Use the log that you have on your calculator.
\[7^{x}=213\]Now using the rules for logs.\[x \log 7= \log 213\] This is where your calculator comes in:\[x.845 = 2.328 \]\[x=2.328\div .845\]
x=2.755

Answer 12

If your calculator has a key that is labeled:\[x ^{y}\]You can verify your answer by entering 7 and then press that key and enter 2.755 and you will get 213.

Answer 13

I don't understand

Answer 14

Do you have a calculator with logs?

Answer 15

yes

Answer 16

Do understand how you got down to \[7^{x}=213\]

Answer 17

yes

Answer 18

Do you know the log rules?

Answer 19

maybe... idk

Answer 20

Well the one that you need to know for this problem is to convert a number with an exponent to a log, which is what we have here you simply take the exponent times the log of the number. Here the exponent is x and our number is 7.
xLog 7 is x 0.845. use your log key and 7 on the calculator. What do you get?

Answer 21

.84509

Answer 22

yes and we don't know what x is yet so on the left side we will put
.84509x
x.84509 just like algebra.

Answer 23

For the right side we simply use the log key and enter 213

Answer 24

What did you get for the right side?

Answer 25

2.32

Answer 26

So we now have
.84509x = 2.32
Solve like any other algebra equation. by dividing both sides of your equation by .84509 getting x by itself on the left and it value on the right.

Answer 27

2.755

Answer 28

That is correct \[7^{2.2755}=213\]

Answer 29

ooops that should be \[7^{2.755}\]

Answer 30

\[7^{2}=49\]\[7^{3}=343\]

Answer 31

thank you so much!

Answer 32

You're welcome, most calculators have two log function.
One is the "common" logs that use the base 10, that was the one we used.
The other set is called "natural" logs and use an irrational number called "e" and it is 2 something.

Answer 33

Good luck with your studies.

Answer 34

and either the common or natural logs would have resulted in the same answer.