How to Solve Exponential Equations | Same Base or Take Logs

How to solve exponential equations — equations with x up in the power — with five worked examples, including the hidden quadratic and the root you have to throw away. There are only two methods, and one question tells you which to use: can I write both sides with the same base? 2ˣ = 32 you can do in your head, because 32 is 2⁵. 2ˣ = 30 you can't, because 30 isn't a power of anything — so that one needs logs. The last example is the one worth staying for. 2^(2x) − 3(2ˣ) − 4 = 0 hides a quadratic. Substitute y = 2ˣ and it factorises — but one of the two roots is negative, and an exponential can never output a negative number. That root gets rejected, not answered. 0:00 2ˣ = 32 vs 2ˣ = 30 — the only decision in this topic 0:57 The two methods: same base, or take logs 1:26 Finishing the hook, and the size check that catches typos 2:02 Example 1 — 3ˣ = 81 2:16 Example 2 — 4ˣ = 8, finding a base they share 2:56 Example 3 — the bracket that loses marks 3:51 Example 4 — when you have to take logs (and ln) 4:47 Example 5 — the hidden quadratic, and the rejected root Previous video Laws of Logarithms:    • Laws of Logarithms Explained | A Log IS a ...