Question

Solve ln 5 + ln (2x) = 5. Round your answer to the nearest hundredth.

Answer 1

First you need to isolate the term with an x, so the idea here is to get rid of the ln5 on left side.
Take note that ln5 is being added on left side, so we need to use the opposite operation of Addition, which is?

Answer 2

Subtraction. :>

Answer 3

You can also combine the natural logs via
\[\ln(a)+\ln(b)=\ln(a \times b)\]

Answer 4

Yes, wait.. we could use the property: lna + lnb = ln(ab) first.

Answer 5

For example ln3 + ln(4x) = ln12x..follow?

Answer 6

I follow! So it'd be ln 5 + ln(2x) = ln10x?

Answer 7

yes correct

Answer 8

Yes, exactly!

Answer 9

Then, we could use the opposite of natural logarithm..

Answer 10

Take note that e^(lnu) = u.

Answer 11

So far our equation is ln(10x) = 5.
For example if we have ln(7x) = 4:
e^(ln(7x)) = e^4 ---> 7x = e^4.

Answer 12

Does that make sense?

Answer 13

I think so, yes.

10x = e^5, then?

Answer 14

Exactly!

Answer 15

Then, we just need to get rid of the 10 on left side, what is the opposite operation of multiplication?

Answer 16

Division!

Answer 17

Yes, so what will we have if we divide 10 on both sides?

Answer 18

x = (e^5)/10

Answer 19

Yes, and if we will calculate that and round to nearest hundredth?

Answer 20

Which is 14.84!

Answer 21

Perfect! Good job!

Answer 22

Thanks! You were a lot of help!

Answer 23

Pleasure to help you! God bless you!

Answer 24

You, too! Have a great night!

Answer 25

You too!