Take the Log

Some exponential equations have no same-base trick. In 2^x = 10, the 10 is not a power of 2: 2^3 = 8 and 2^4 = 16, so x sits somewhere between 3 and 4, and no whole number works.

A log names that number. It asks for a power, so log_2(2^x) is simply x. Taking log base 2 of both sides turns 2^x = 10 into x = log_2(10). The base of the log is always the base of the power.

log_2(10) is the exact answer. A calculator gives about 3.32, which is a rounded copy of the same number. Keep the exact form, just as you keep √(2) rather than 1.41.