Properties of logarithms Assume logbx...

Question

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logbx²

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given that log base A of P is equal to 0.45 evaluate the expression log base A of P to the power of three. Awesome. So it appears our final answer that we're ultimately trying to solve for for this specific prompt is we're trying to evaluate the expression log base A of P to the power of three. So with that in mind, let's read off multiple choice answers to see what our final answer might be. A is 1.50 B is 1.25 C is 0.45. And finally D is 1.35. Awesome. So our first step is we need to identify all of our given variables and the target variable that we're trying to ultimately solve for. So we're told that log base A of P is equal to 0.45. And our target variables are trying to figure out log base a of P to the power of three. So now we need to recall and use the log property that states that log base A of P to the power of K is equal to K multiplied by the log base A. So K multiplied by log base A of P. Awesome. So now all we need to do is plug in our known variables indoor equation or rather substitute in our given value indoor equation. So we need to take log base A. So we need to take log base a of P to the power of three. And we need to say that this is equal to three multiplied by log base a of P. So with that in mind, we can now plug in our non variables when you take three, multiplied by 0.45. And when we take three multiplied by 0.45 we will find that this is equal to 1.35 and that is our final answer. Hooray, we did it. So therefore, without a doubt, our final answer has to be log base A of P to the power of three is equal to 1.35. And this value corresponds to multiple choice answer letter D which once again is 1.35. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logbx²

Key Concepts

Properties of Logarithms

Power Property of Logarithms

Base of Logarithm

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