Textbook Question
Write each equation in its equivalent exponential form. 2 = log9 x
1023
views
6. Exponential & Logarithmic Functions
Introduction to Logarithms
1:46 minutesProblem 11
Textbook Question
Write each equation in its equivalent logarithmic form. 2-4 = 1/16
Verified step by step guidance1
Identify the components of the exponential equation \(2^{-4} = \frac{1}{16}\). Here, the base is 2, the exponent is -4, and the result is \(\frac{1}{16}\).
Recall the definition of logarithms: If \(a^x = b\), then the equivalent logarithmic form is \(\log_{a} b = x\).
Apply this definition to the given equation by setting \(a = 2\), \(b = \frac{1}{16}\), and \(x = -4\).
Write the logarithmic form as \(\log_{2} \left( \frac{1}{16} \right) = -4\).
This expresses the original exponential equation in its equivalent logarithmic form.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential and Logarithmic Forms
An exponential equation like a^x = b can be rewritten in logarithmic form as log_a(b) = x. This conversion helps in solving for exponents by expressing the relationship between the base, exponent, and result in terms of logarithms.
Recommended video:
5:02
Solving Logarithmic Equations
Properties of Exponents
Understanding how exponents work, including negative exponents, is essential. For example, a negative exponent indicates the reciprocal of the base raised to the positive exponent, such as 2^-4 = 1/(2^4) = 1/16.
Recommended video:
Guided course
04:06Rational Exponents
Logarithm Definition and Notation
A logarithm log_a(b) answers the question: 'To what power must the base a be raised to get b?' Recognizing this definition allows one to rewrite exponential equations into logarithmic form accurately.
Recommended video:
7:30Logarithms Introduction
Related Videos
Related Practice