Use the various properties of exponential and logarithmic functio...

Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^(2 log_2 2))

Accepted Answer

Hello, everyone. We've been asked to find the value of F of three raised to the three multiplied by log base three of three power for the function given below the function is F of X equals log base three of X. Our answer choices are a three B 27 C one D, the natural log of three. First, I'm looking at this as function notation. So I have F of three raised to the three log base three of three power, which means I need to place that value in for X in our F of X function. So this means I have the log base three of three raise to the three log base three of three. Now, there's a couple different ways you can go about this problem. I'm gonna take it little by little. First. I'm gonna look in my exponent at the log base three of three. I recall that when I have a log and the base matches the value we're taking the logarithm of that, this equals one. So this can be written as log base three of three raised to the third power because three times one is three from there I again can think about this in terms of using some of my logarithm rules. I recall that if I have an exponent on the value, I want to take the logarithm of I can move it to the front and it becomes a coefficient. So this can be rewritten as three log base three of three. Next, we're gonna use that base rule again. So this section, so log base three of three again is gonna equal one. So we will have three multiplied by one, which is three. So our answer is three. Despite all of those logs and exponents, our answer choice A of three is our answer. Have a nice day.

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Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^(2 log_2 2))