2log[base3]9 = ?

since 9=3^2,

log_3(9) = 2
So, 2log_3(9) = 2*2 = 4

Thx

To find the value of 2log[base3]9, we need to understand what logarithms are and how they work.

A logarithm is the inverse operation of exponentiation. It helps us find the exponent to which a given base must be raised to obtain a specific number. In this case, we have the logarithm with a base of 3.

The expression 2log[base3]9 can be rewritten in exponential form as 3 raised to the power of what gives us 9, and then multiplied by 2. So, we want to find x in the equation: 3^x = 9.

To solve this equation, we can use the fact that 9 is equal to 3^2. Therefore, we can rewrite the equation as: 3^x = 3^(2).

To solve for x, we set the exponents equal to each other: x = 2.

Now, we can substitute this value of x back into the original expression: 2log[base3]9 = 2 * 2 = 4.

So, the value of 2log[base3]9 is 4.