Textbook Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
log5 (7 × 3)
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Ch. 4 - Exponential and Logarithmic Functions
Chapter 5, Problem 3
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5^x=125
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Equations
Exponential equations are mathematical expressions where variables appear in the exponent. To solve these equations, one common method is to express both sides with the same base, allowing for the exponents to be equated. This approach simplifies the problem and makes it easier to isolate the variable.
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Solving Exponential Equations Using Logs
Base and Exponent
In an exponential expression, the base is the number that is raised to a power, while the exponent indicates how many times the base is multiplied by itself. Understanding the relationship between bases and exponents is crucial for manipulating exponential equations, as it allows for the conversion of numbers into a common form for comparison.
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7:39Introduction to Exponent Rules
Equating Exponents
When both sides of an exponential equation are expressed with the same base, the next step is to equate the exponents. This principle arises from the property that if a^m = a^n, then m must equal n, provided that a is not zero. This step is essential for solving the equation and finding the value of the variable.
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04:06Rational Exponents
Related Practice
Textbook Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64
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Textbook Question
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 3.
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Textbook Question
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5
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Textbook Question
In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 x
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Textbook Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
log7 (7x)
333
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