What is x if log2 (3+log3(x))=2? 2,3 are bases of logarithms

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shaznl1's profile pic

Posted on

If log 2 (3+ log 3 (x))= 2

then it means that 2^2=(3+log 3 x)

2^2 =4

4=3+log 3 (x)

Subtract three to both sides

1= log 3 (x)

using the definition of logs again

3^1 = x

x= 3

The only value accepted was a solution to this eqaution is x=3

 

Actually, log just mean the opposite of exponents, so when you take off a log a where a as the base, exponent the other side with "a".

You can checkyour answer by plugging it in and see if it matches the definition of logs

giorgiana1976's profile pic

Posted on

First, we'll impose constraints of existence of logarithms:

x>0

3 + log3 (x)>0

log3 (x) > -3

log3 (x) > log3 (3^-3)

log3 (x) > log3 (1/3^3)

x > 1/27

Now, we'll solve the equation taking antilogarithm:

3 + log3 (x) = 2^2

We'll subtract 3 both sides:

log3 (x) = 4 - 3

log3 (x) = 1

We'll take antilogarithm again:

x = 3^1

x = 3

Since x = 3 > 1/27, therefore the value of x is accepted as solution of the given equation: x = 3.

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