SOLUTION: I just need someone to explain this and why 2 is the answer: 3^(log base 9 (4))= 2 I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.

Question 1057131: I just need someone to explain this and why 2 is the answer:
3^(log base 9 (4))= 2
I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.
Found 4 solutions by solve_for_x, josgarithmetic, ikleyn, MathTherapy:
Answer by solve_for_x(190)   (Show Source): You can put this solution on YOUR website!
When you have something like log (base 9) 4, you can rewrite it as

And when you do that, you can use any base for the logarithms that you want.

So, instead of using the common base-10 log, we can write is using a base-3 log:

But log3 (9) = 2:

Substituting in place of gives:

which equals:

And since , the expression is equal to:

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
3^(log(9,4))=2

?

Look into that . Change of Base formula might be helpful....

Look in table of logs or use calculator:

, and you might use logs table again...
Result is something extremely close to 2.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
I just need someone to explain this and why 2 is the answer:
3^(log base 9 (4))= 2
I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.
~~~~~~~~~~~~~~~~~~~~~~~

The problem is solved in two steps:

1. = Indeed, if = x, it means (by the definition of logarithm) that = 2. Then = = 4, which implies = 4, which is the same as = 4, or = 4. The last equality means that = x. Hence, = , QED. 2. = 2. (<---- = x for any x > 0 and for any b > 0, b=/= 1. This is the basic property of the logarithm, equivalent to the definition of the logarithm)

On logarithms, see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
I just need someone to explain this and why 2 is the answer:
3^(log base 9 (4))= 2
I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.

Let
------- Converting from EXPONENTIAL to LOGARITHMIC form
------- Changing right side to base 3, by applying CHANGE OF BASE
------- Changing to 2
----- Cross-multiplying
------ Applying to left-side of equation
------ Equating expressions since log bases are the same

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