SOLUTION: What is the value of x? https://i.ibb.co/5FdV518/2.jpg (Sorry I don't know how to type this up. I looked at the guide but still can't get it right.)

Question 1204568: What is the value of x?
https://i.ibb.co/5FdV518/2.jpg
(Sorry I don't know how to type this up. I looked at the guide but still can't get it right.)
Found 3 solutions by josgarithmetic, math_tutor2020, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
log(9,3*sqrt(3))=x

--

same base both sides so the exponents are equal.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

To type on a keyboard, you could write log(9,x)

So something like would be log(9, 3*sqrt(3) )

Now onto the problem at hand.

Convert the equation to exponential form

Rewrite 9 as 3^2. Rewrite the square root as an exponent of 1/2.

Use the rule that (a^b)^c = a^(b*c)

Use the rule that a^b*a^c = a^(b+c)

Since the bases are both 3, the exponents must be equal.

-----------------------------

Another approach would be to use the change of base formula.

Change of base formula is applied here. From this point onward, the logs are base 10.

Use the log rule log(A^B) = B*log(A)

Your steps do not have to be as verbose as shown above.

As quick confirmation, use a calculator to find that:
log(3*sqrt(3))/log(9) = 0.75

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

A different approach -- easier, in my opinion...

Use

For this problem, we have

In this expression we can use any base we want. Since all the numbers are powers of 3, use log base 3.

ANSWER: 3/4

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