If 8^a = 16^b, then the ratio of a to b is _____?
- 1/2
- 4/3
- 3/4
- None of these
Explanation
8^𝑎 = 16^𝑏
We can rewrite 16 as 2^4, so:
(2^3)^𝑎 = (2^4)^𝑏
Using the power rule (a^m)^n = a^(mn), we get:
2^(3𝑎) = 2^(4𝑏)
Since the bases are equal (both are 2), we can equate the exponents:
3𝑎 = 4𝑏
Now, divide both sides by 3𝑏:
𝑎/𝑏 = 4/3
So, the ratio of 𝑎 to 𝑏 is 4:3 or 4/3.
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