Find x if Log_x(9/25) = 2

Question

Accepted Answer

{"content":[{"content":[{"text":"Step 1 (Convert to Exponential Form):","type":"text","marks":[{"type":"bold"}]},{"text":" The equation ","type":"text"},{"attrs":{"latex":"\log_x(9/25) = 2"},"type":"math_inline"},{"text":" is rewritten in exponential form as:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"x^2 = \frac{9}{25}"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Solve for x):"},{"type":"text","text":" Taking the square root of both sides:"}],"type":"paragraph"},{"attrs":{"latex":"x = \pm \sqrt{\frac{9}{25}} = \pm \frac{3}{5}"},"type":"math_block"},{"content":[{"text":"Since the base of a logarithm must be strictly positive (","type":"text"},{"attrs":{"latex":"x > 0"},"type":"math_inline"},{"text":" and ","type":"text"},{"attrs":{"latex":"x \neq 1"},"type":"math_inline"},{"type":"text","text":"), we discard the negative solution."}],"type":"paragraph"},{"attrs":{"latex":"x = \frac{3}{5} = 0.6"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The value of ","type":"text"},{"attrs":{"latex":"x"},"type":"math_inline"},{"text":" is exactly ","type":"text"},{"type":"text","marks":[{"type":"code"}],"text":"0.6"},{"text":" (or ","type":"text"},{"text":"3/5","type":"text","marks":[{"type":"code"}]},{"text":").","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution