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) = 3^x, find ƒ(log_3 (ln 3))

Accepted Answer

Hello, everyone. We've been asked to find the value of F of log base four of the natural log of 16. For the function given below the function is F of X equals four raised to the X power. Our answer choices are a, the natural log of 16 B C four or D four natural log of 16. First recall that in function notation, we're given F of the log base four of the natural log of 16. This means we need to put log base four of the natural log of 16 in for X in our F of X function. So this means we have a base of four and then our exponent is log base four natural log 16. Recall the rules about logarithms and that if we have a base raised to a logarithmic exponent of the same base, those pieces will cancel out and our answer will be the rest of the exponent, which in this case is the natural log of 16, there's no reason to go any farther. We have not enough information to continue this. So this is our answer. The natural log of 16, which is answer choice. A 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) = 3^x, find ƒ(log_3 (ln 3))