Solving Exponential and Logarithmic Equations Answers
Because the are equal
What equation is equivalent to 9x - 3 = 729?
Solve: 9x - 3 = 729x =
6
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Select all of the potential solution(s) of the equation 2log5x = log54.
Which equation is equivalent to log5x3 - logx2 = 2?
What is the solution to ln (x2 - 16) = 0?
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Consider the equation log(3x - 1) = log28. Explain why 3x - 1 is not equal to 8. Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.
In the equation log(3x - 1) = log2(8), 3x - 1 is not equal to 8 because the logarithms have different bases; the left side is the common logarithm (base 10) while the right side is base 2. To solve the equation, first simplify the right side: log2(8) = 3 because 2 to the third power is 8. This results in the equation log(3x - 1) = 3. Next, rewrite the logarithmic equation in exponential form using base 10: 3x - 1 = 10^3. Therefore, 3x - 1 is equal to 1000. To find x, add 1 to both sides and divide by 3 (x = 1001/3).
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, the must also be equal.
Solve: log5x3 - logx2 = 2 x =
20
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