Subject: having trouble with a problem Name: Beth Who are you: Teacher Having trouble solving and explaining the following problem to my group of Algebra 2 students. any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!! log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Thanks We have two responses for you. Hello Beth. Let's say y = log4(x). Then 4y = x. In other words, x = 22y. Now take the log in base 2 of each side: log2(x) = log2 (22y) = 2y (log2 (2) ) = 2y = 2 log4(x). So you can substitute log4 (x) with (1/2) log2 (x). Repeat as needed to solve for x. Hope this helps, Stephen La Rocque. and Beth, You need to start by getting rid of the logs. You have 256log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 2567/4. Simplify the right hand side by first taking a 4th root. As for the left hand side, since the bases involved are powers of 2, you can break it into a product of 4 parts, the first of which is 256log256(x) = x, the next is 256log16(x) = 162log16(x) = x2 and so on. You should end up with x13 and then you can solve for x. Penny