Solve for x:
3^(2x)=14
We've gotten:
2x=log(subscript 3)14=2.4
Is this two answers, or what?
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To solve for x in the equation 3^(2x) = 14, you correctly took the logarithm base 3 of both sides. However, there seems to be a slight error in the value you provided for log(subscript 3)14. Let's go through the solution step by step.
1. Start with the equation: 3^(2x) = 14.
2. Take the logarithm base 3 of both sides to bring down the exponent: log(subscript 3)(3^(2x)) = log(subscript 3)14.
3. Apply the logarithmic property log(subscript b)(b^x) = x: 2x = log(subscript 3)14.
4. Now, divide both sides by 2 to isolate x: x = (1/2) * log(subscript 3)14.
To find the numerical approximation for x, you would need to evaluate log(subscript 3)14.
Using a calculator or computer software, you can find that log(subscript 3)14 ≈ 2.251.
Hence, x ≈ (1/2) * 2.251 = 1.125.
Therefore, the approximate value for x in the equation 3^(2x) = 14 is x ≈ 1.125.