Logarithm Equality sqrt(log_x(sqrt(3x))} * log_3 x = -1 I am not entirely sure how to go about solving for x. I cannot square each side because the product isn't >=0, I can't think of any more approaches right now.
Sara Fleming
Answered question
2022-09-23
Logarithm Equality
I am not entirely sure how to go about solving for . I cannot square each side because the product isn't , I can't think of any more approaches right now.
Answer & Explanation
Santiago Collier
Beginner2022-09-24Added 8 answers
Since square roots are nonnegative, we know that so that . Now let and let . Then by using log rules, our equation becomes:
Converting back, we find that either or so that either or . But then since , we reject the first extraneous solution and conclude that
misyjny76
Beginner2022-09-25Added 1 answers
Will things look better without logarithms in the equation? First, let's simplify
Now, we'll use the info from Ciapan's comment: . The equation now becomes
Can you solve that? You may want to check your answers after to make sure they make sense.