25^x + 5^(1+2x) = 40 Find the exact solution of the exponential equation in terms of logarithms.
Added by Jeffrey L.
Step 1
So, the equation becomes 5^(2x) + 5 * 5^(2x) = 40. We can factor out 5^(2x) to get 5^(2x) * (1 + 5) = 40. Simplifying, we get 5^(2x) * 6 = 40. Dividing both sides by 6, we get 5^(2x) = 40/6 = 20/3. Taking the natural logarithm of both sides, we get Show more…
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