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 (2 ln 3))

Accepted Answer

Hello, everyone. We've been asked to find the value of F of log base four of three times the natural log of four for the function given below the function is F of X equals four raised to the X power. Our answer choices are a three times the natural log of four B four multiplied by the natural log of three C. The natural log of three D, the natural log of four recall that in function notation, when we're given something like F of log base four of three multiplied by the natural log of four, this means we are going to put the log base four of three times the natural log of four in for the X value in the F function. So this means we have four raised to the log base four of three multiplied by the natural log of four power. Recall that when we have a base raised to a logarithmic power, if the log base matches the exponential base, they cancel out leaving us with the rest of the exponent as part of our answer. So we have three multiplied by the natural log of four left. Once those cancel out from here. We need to decide, can this be solved any farther or should I leave it? As is for this example, there's nothing left we can solve. So this is our answer three multiplied by the natural log of four, 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 (2 ln 3))