Question

Help please again @kirbykirby

Answer 1

sure

Answer 2

What is the solution to the equation \[14^{x + 3} = 21\]

Answer 3

First step: log both sides
Then you can use the property on the left side: \[\large \log(a^x)=x\log a \]

Answer 4

Alright could you show me please not a big fan of log

Answer 5

\[ \Large \log(14^{x+3})=\log 21\\
\, \\(\Large x+3)\log14=\log 21\]

Answer 6

do you see how I applied the rule above to your equation?

Answer 7

What is next

Answer 8

\(\bf 14^{x + 3} = 21
\\ \quad \\
\textit{log cancellation rule of }log_{\color{red}{ a}}({\color{red}{ a}}^x)=x\qquad thus
\\ \quad \\
14^{x + 3} = 21\implies log_{\color{red}{ 14}}({\color{red}{ 14}}^{x + 3})=21\implies ?\)

Answer 9

woops

Answer 10

\(\bf 14^{x + 3} = 21
\\ \quad \\
\textit{log cancellation rule of }log_{\color{red}{ a}}({\color{red}{ a}}^x)=x\qquad thus
\\ \quad \\
14^{x + 3} = 21\implies log_{\color{red}{ 14}}({\color{red}{ 14}}^{x + 3})=log_{\color{red}{ 14}}21\implies ?\)

Answer 11

\(\log 14\) is just a number, so you can distribute \((x+3)\log 14\) as you do with any regular number:
\((x+3)\log 14 = x\log 14 + 3 \log 14\)

Answer 12

So what is the next step to finding x

Answer 13

\[ x\log 14 + 3 \log 14=\log 21\] Subtract \(3 \log 14\) from both sides

Answer 14

(actually you can use @jdoe0001 's method too if you prefer it)

Answer 15

So the problem will appear to be x log 14 log 14 = log 18

Answer 16

oh be careful. I'm not sure what you did there.
\[ x\log 14 + 3 \log 14 = \log 21\\
x \log 14 + 3 \log 14 \color{red}{-3\log 14}=\log 21 \color{red}{-3 \log 14}\\
x \log 14 = \log 21 - 3 \log 14\]

Answer 17

ohhh okay next step please (hate log so much do we even use it in the real world)

Answer 18

euh yes lol it is used.. but depends on which field you'd go into

Answer 19

In what field exactly?

Answer 20

The thing is you can't add/subtract the thing in the log( .. ) with other log's ( ..) if the number in the ( ..) is not the same:
\(\log 2 + \log 3 \ne \log (2+3)\)

If the number is the same, then you treat log "like" if it was a variable, or a radical:
\(\log 3 + \log 3 = 2 \log 3\)

Answer 21

Math, physic, engineering, computer science, meteorology, statistics... and others I can't think of lol

Answer 22

What about business world

Answer 23

It comes up too in finance.. with exponential functions (interest rates)

Answer 24

Okay what is next to solve for x (Now I have to pay attention closely now)

Answer 25

the last step though for your problem should be straightforward:
\[ x \log 14 = \log 21 - 3 \log 14\]
Since \( \log 14\) is just a number, you can isolate x by just dividing both sides by \(\log 14\)

Answer 26

The whole other side of the problem

Answer 27

I got three if I was right @kirbykirby still there?

Answer 28

Wait I got -1.846

Answer 29

yes! :)

Answer 30

Thanks so much but do you know any good websites that tech log for free

Answer 31

if you do mail to me please

Answer 32

Perhaps here: http://tutorial.math.lamar.edu/Classes/Alg/LogFunctions.aspx