Solve the equation

Question

4^x-2^x-6=0

Answer 1

4^x-2^x-6=0 can be solved by use of a substitution technique, as described below.

Since 4 = 2² we can write this as 2^2x - 2^x - 6 = 0.  Rewrite the first term as the square of 2^x.

Let z = 2^x; rewriting the equation gives z² - z - 6 = 0; this you can solve, by factoring, for z.

Next, drop any z value that is negative and solve for x, given that that z = 2^x, by taking logarithm (base 2)--you'll need the 'change of base' formula, possibly.