Problem 5
Question
The Inverse Properties of logarithms and exponentials state that \(\log _{a} a^{x}=x\) and _____.
Step-by-Step Solution
Verified Answer
The second inverse property of logarithms and exponentials is \( a^{(\log_a x)} = x \)
1Step 1: Identify the Inverse Property
We are given the inverse property of logs and exponentials which states that \( \log_a(a^x) = x \). The task is to find the other inverse property.
2Step 2: Recall the Second Inverse Property
Recall that another inverse property for logarithms and exponentials is \( a^{(\log_a x)} = x \)
Other exercises in this chapter
Problem 5
Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(4^{2 x-7}=64\) (a) \(x=5\) (b) \(x=2\)
View solution Problem 5
Match the property of logarithms with its name. (a) Power Property (b) Quotient Property (c) Product Property $$\ln u^{n}=n \ln u$$
View solution Problem 6
A logistic curve is also called a ________ curve.
View solution Problem 6
Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(2^{3 x+1}=32\) (a) \(x=-1\) (b) \(x=2\)
View solution