0 like 0 dislike
0 like 0 dislike
If 47^x= 30, what is the value of x?

7 Answers

0 like 0 dislike
0 like 0 dislike
Why is this NSFW
0 like 0 dislike
0 like 0 dislike
You have to take the logarithm of both sides. You get:

log(47\^x) = log(30)

Now, we know that:

log(a\^b) = b \* log(a)

So we can rewrite it to:

x\*log(47) = log(30)

Thus x:

x = log(30)/log(47)

Which is approximately:

x = 0.8834
0 like 0 dislike
0 like 0 dislike
Is it NSFW because the answer is actually 0.5318008?
0 like 0 dislike
0 like 0 dislike
I see that some people try to solve this in ways I believe are more complex than required.

The answer may be given directly as log in base 47 of 30, *by definition of logarithm*.

The only problem is that calculators do not have "log in base 47", but you can apply change of base formula and calculate that as log\_A(30)/log\_A(47), where log\_A is logarithm in base A. A may be any base for which your calculator can do logarithms.
0 like 0 dislike
0 like 0 dislike
* 47^x = 30
* Log47( 47^x ) = Log47( 30 )
* xLog47( 47 ) = Log47( 30 )   <\[Log47( 47 ) = 1\]>
* x =  Log47( 30 )
0 like 0 dislike
0 like 0 dislike
hmm
 
                47^x = 30
                log_47 (47^x) = log_47 (30)
                x = log_47 (30)

A concept to consider here is the *inverse* of a function.

What is an inverse of a function?

In a nutshell, if two functions f and g are inverses of each other, then if we call f with the output of g evaluated for some input, we should get that input back in return; and likewise, if we call g with the output of f evaluated for some input, we should get that input back in return.

So simple example, say f(x) and g(x) are inverses, then what is f(g(x)) and g(f(x))?

They’re both x.

With this, a simpler notation for the above you might see is, (f o g)(x) = f(g(x)) = x iff f and g are inverses. Likewise, (g o f)(x) = g(f(x)) = x iff f and g are inverses.

So now then, your situation

                47^x = 30
                log_47 (47^x) = log_47 (30)
                x = log_47 (30)

How did we know to do the 2nd step?

Well it turns out, an exponential function and log function are inverses if the base of the exponential is the same base as the log.

For example, we have 47^x = 30

The base of this exponential is 47. While there is no log, we can make one, where it’s base is also 47 and do this to both sides!

            
                log_47 (47^x) = log_47 (30)
                

Now, recall the exponential and log now are inverses, they have the same base. We could then think of this in terms of the other inverses we talked about.

Say f(x) = 47^x and g(x) = log_47 (x)

Then, f(g(x)) = g(f(x)) = x.

That is, the rule you see above is taking the log of each side with the same base of the exponent, that is g(f(x)) = log_47 (47^x) = x

Which is why you saw the final step

                log_47 (47^x) = log_47 (30)
                x = log_47 (30)



The other rule, not seen in this problem is this one, f(g(x)) = 47^(log_47 (x)) = x. This is called the **exponentiation** rule.

If we exponentiate - make a base that is the same as that of the log’s base and raise that base to the power of the log, then we get x (whatever is inside the parenthesis).

So hopefully that puts more clarification on the table. What is going on, how did we know to do that rule, where that rule comes from / relates to.
0 like 0 dislike
0 like 0 dislike
I thought it was r/askreddit

If it wasn't log , I could have done it

Related questions

0 like 0 dislike
0 like 0 dislike
1 answer
MSR_Tlse asked Jun 21
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
MSR_Tlse asked Jun 21
0 like 0 dislike
0 like 0 dislike
20 answers
balkissoon asked Jun 21
Considering leaving the actuarial profession. What are some interesting fields you've heard of former actuaries going into? How did they get into the new field?
balkissoon asked Jun 21
0 like 0 dislike
0 like 0 dislike
9 answers
HilaryKHarper asked Jun 21
Has anyone successfully guessed on like half of the questions on an exam and still passed?
HilaryKHarper asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
LondonAssembly asked Jun 21
The Actuarial Education Company finally removed the dictionary definition of "final solution" from their binders
LondonAssembly asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
driveshift asked Jun 21
I did this all wrong but got the right answer? Took half of .075, used d=(1+i)/i to get discount rate, and just added. Decimal was off, but i got the numbers right. Luck?...
driveshift asked Jun 21

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!