MTH-100 Lecture Notes - Lecture 42: Exponential Function, Scientific Calculator
Document Summary
A simple example of an exponential equation is 2x = 16 (variable is in the exponent) To solve we can use inspection, x = 4. What if we have 2x+3 = 25 ? because the bases are the same, we can see that if bm = bn then m and n must be equal. 2x+3 = 25 x + 3 = 5 x = 2. Drop the 2"s x +5 = 4(x 1) x + 5 = 4x 4. So, in general, if the bases are equal, set exponents equal and solve. If possible, rewrite one or both bases to use the same base, then follow as above: 5x+5 = 53x-1, 32x = 27x-4. To solve take the log (any base) of both sides. Check: 52. 43 50 (more decimal places in answer, closer estimate) We get the same answer with log and ln or a log of any other base. log(5 ) log 50 x log 5 log 50 x.
