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.

Answered: Image /qna-images/answer/5e675a7f-e5d6-4c69-aea0-a62c23a38dde.jpg

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)

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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