Solve: log2 √(x+5)=4

Name: Problem 35, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-12-18T01:30:18-08:00
Duration: 2 min 18 s
Channel: Sirat Shah
Description: Solve: log2 √(x+5)=4

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Key Concepts

Domain Restrictions

Both logarithmic and square root functions have inherent domain restrictions. For logarithms, the argument must be positive, and for square roots, the radicand must be non-negative. Recognizing these restrictions is important to ensure that the solutions to the equation are valid within the context of the functions involved.

Logarithmic Equations

Logarithmic equations involve an unknown variable inside a logarithm. The fundamental concept is that if log_b(a) = c, then it can be rewritten in exponential form as b^c = a. This conversion is crucial for solving logarithmic equations by isolating the variable after transforming the equation into an exponential format.

Exponential Equations

Exponential equations emerge when an equation in logarithmic form is rewritten as b^c = a. This process leverages the definition of logarithms and simplifies the problem to a format where standard algebraic techniques, such as isolating the variable, can be applied.

Square Root Function

The square root function, denoted by ?, represents the principal (non-negative) square root of a number. In equations, it is essential to recognize that squaring both sides of an equation is a common technique used to eliminate the square root, but care must be taken regarding the domain and possible extraneous solutions.

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