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Choose which statements support correct reasoning when solving the equation 52x+3 = (√√5)² x+4 After choosing all correct statement(s) of algebraic reasoning, determine the final solution to the equation. Select all that apply.

Choose which statements support correct reasoning when solving the equation 52x+3 = (√√5)² x+4 After choosing all correct statement(s) of algebraic reasoning, determine the final solution to the equation. Select all that apply.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Choose which statements support correct reasoning when solving the equation \[ 5^{2x+3} = (\sqrt{5})^{x+4} \] After choosing all correct statement(s) of algebraic reasoning, determine the final solution to the equation. Select all that apply. - □ \( \log_5(5^{2x+3}) = \log_5(\sqrt{5})^{x+4} \) which leads to \[ 2x + 3 = x + 4 \] - □ \[ x = \frac{1}{3} \] - □ \((\sqrt{5})^{4x+3} = (\sqrt{5})^{x+4}\) which leads to \[ \log_{\sqrt{5}} (\sqrt{5})^{4x+3} = \log_{\sqrt{5}} (\sqrt{5})^{x+4} \] - □ \[ x = -\frac{2}{3} \] - □ \((\sqrt{5})^{4x+6} = (\sqrt{5})^{x+4}\) which leads to \[ x = -\frac{1}{2} \]
Transcribed Image Text:Choose which statements support correct reasoning when solving the equation \[ 5^{2x+3} = (\sqrt{5})^{x+4} \] After choosing all correct statement(s) of algebraic reasoning, determine the final solution to the equation. Select all that apply. - □ \( \log_5(5^{2x+3}) = \log_5(\sqrt{5})^{x+4} \) which leads to \[ 2x + 3 = x + 4 \] - □ \[ x = \frac{1}{3} \] - □ \((\sqrt{5})^{4x+3} = (\sqrt{5})^{x+4}\) which leads to \[ \log_{\sqrt{5}} (\sqrt{5})^{4x+3} = \log_{\sqrt{5}} (\sqrt{5})^{x+4} \] - □ \[ x = -\frac{2}{3} \] - □ \((\sqrt{5})^{4x+6} = (\sqrt{5})^{x+4}\) which leads to \[ x = -\frac{1}{2} \]
The image contains a series of mathematical equations with multiple-choice options. Here is the transcription: **Option 1:** - \((\sqrt{5})^{4x+6} = (\sqrt{5})^{x+4}\) - which leads to: - \(\log_{\sqrt{5}} ((\sqrt{5})^{4x+6}) = \log_{\sqrt{5}} ((\sqrt{5})^{x+4})\) **Option 2:** - \(x = \frac{1}{2}\) **Option 3:** - \(x = \frac{2}{3}\) **Option 4:** - \(5^{2x+3} = 5^{\frac{1}{2}(x+4)}\) - which leads to: - \(\log_{5} (5^{2x+3}) = \log_{5} (5^{\frac{1}{2}(x+4)})\) **Option 5:** - \(x = -\frac{1}{2}\) There are no graphs or diagrams in the image; only mathematical equations are presented.
Transcribed Image Text:The image contains a series of mathematical equations with multiple-choice options. Here is the transcription: **Option 1:** - \((\sqrt{5})^{4x+6} = (\sqrt{5})^{x+4}\) - which leads to: - \(\log_{\sqrt{5}} ((\sqrt{5})^{4x+6}) = \log_{\sqrt{5}} ((\sqrt{5})^{x+4})\) **Option 2:** - \(x = \frac{1}{2}\) **Option 3:** - \(x = \frac{2}{3}\) **Option 4:** - \(5^{2x+3} = 5^{\frac{1}{2}(x+4)}\) - which leads to: - \(\log_{5} (5^{2x+3}) = \log_{5} (5^{\frac{1}{2}(x+4)})\) **Option 5:** - \(x = -\frac{1}{2}\) There are no graphs or diagrams in the image; only mathematical equations are presented.
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