simplify 3^(2log3[5])
To simplify the expression 3^(2log3[5]), we can start by using the logarithm properties to rewrite 2log3[5].
Recall that log base b of a to the power of n is equal to n times log base b of a. Using this property, we can rewrite 2log3[5] as log3[5^2].
Now, rewriting the expression as log3[5^2] is helpful because it allows us to simplify further. The log3 function tells us the exponent we need to raise the base 3 to in order to get 5^2. In other words, we want to find the power, x, such that 3^x = 5^2.
To find this power, we can use the property of logarithms that states if log base b of a equals log base b of c, then a equals c. Applying this property, we have 3^x = 5^2.
Now, we can raise both sides of the equation to the power of 1/2 to solve for x:
(3^x)^(1/2) = (5^2)^(1/2)
3^(x/2) = 5
Finally, we can solve for x by taking the logarithm of both sides of the equation with base 3:
log3[3^(x/2)] = log3[5]
x/2 = log3[5]
x = 2 * log3[5]
Therefore, the expression 3^(2log3[5]) simplifies to 3^(x), where x is equal to 2 * log3[5].
well 2log3(5) is log3 (25)
and 3^log3(x) is x
Take it from there.