Logarithms

We are
given that are the -th, -th, and -th terms of a G.P. In a geometric progression, the general form of the -th term is:
where is the first term and is the common ratio. Now, we are dealing with logarithmic expressions involving these terms. To solve the problem, we use the properties of logarithms and the fact that the terms are in G.P. For a G.P. with terms , we have the following relations: since is the geometric mean of and . Taking logarithms of both sides: Now, applying the properties of logarithms, we solve the equation: Thus, the correct answer is .

Step 1:
The reflection of a line across another line involves finding the line's perpendicular bisector and applying the reflection formula. Here, we are reflecting the line across the line .
Step 2:
The general method for reflecting a line involves using the reflection formula, which results in the new equation being:
Step 3:
Therefore, the equation of the image of the line after reflection across is .