Solve for x. 2log2x plus log21 equals log24?

Answer 1

I will assume that the "2" after each log is a subscript (indicating log to the base 2). Basically, you must use the well-known logarithmic identities, a log b = log ba, and log a + log b = log ab.

2 log2x + log21 = log24

log2x2 + log21 = log24

log2x2(1) = log24

log2x2 = log24

Take antilogs on both sides:

x2 = 4

In this last equation, x is either 2 or -2. However, negative numbers are not appropriate for the original equation (assuming real numbers), so the only solution is 2.

For safety, this should be checked in the original equation; I'll leave that part to you.