Determine whether the following statements are true and give a...

Question

Determine whether the following statements are true and give an explanation or counterexample.

$2 = 1 0^{\log_{10} 2}$

Accepted Answer

Welcome back, everyone determine the validity of the given statement. Five equals 19 to the power of log base 19 of five. The two answer choices are a true and B false. So for this problem, we're going to use the property which says that A to the power of log of base A of sum number B is simply equal to B. If we look at the right hand side of the given statement, it says that 19 to the power of log of base 19 of five, right, this is our given, this is part of the given statement and we can notice that it essentially fits the property. Our A value is 19. We have the same number and the same base and B in this case is simply equal to five. So we can simplify this to five based on the property 19 to the power of log base 19 of five is simply equal to five based on this property. So the given statement is true. So the correct answer to this problem is option A. Thank you for watching.

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Determine whether the following statements are true and give an explanation or counterexample.

$2 = 1 0^{\log_{10} 2}$