How do I Find Exponents for a Given Number?
A number R can be written as a base number b raised to the exponent x (b^x). You solve for x by taking loga (log base a) of both sides of R = b^x, giving loga R = loga b^x. Use the logarithmic property loga b^x = x loga b to bring down the exponent to get loga R = x loga b, so x = loga R/loga b. Although x can be calculated using any loga function, calculators offer log base 10 (log10 = log) and the natural logarithm, log base e (loge = ln). The standard equations for finding x are then x = log R/log b or x = ln R/ln b. If x and b are integers and R is small enough, you can usually find the exponent by just trial and error. For example, if R = 125 = 5^x, you don’t need to try many numbers to conclude that 125 = 5*5*5 = 5^3 (* means multiply). If R is a very large number, then use the log formula. For example, if R = 1,953,125 = 5^x, find x by calculating x = log R/log b = log 1,953,125/ log 5 = 6.290730039/0.698970004 = 9 so that 1,953,125 = 5^9. Note that you get the same x value if i
