Final answer:
To find the value for x in the equation log₁₄ 92 = x, we can use the change of base formula. Substituting the values into the formula, we can calculate x as approximately 1.712.
Step-by-step explanation:
To find the value for x in the equation log₁₄ 92 = x, we can use the change of base formula. The formula states that logₐ b = logₓ b / logₓ a. In this case, we can use the common logarithm (log base 10) as the new base. So, substituting the values into the formula, we have:
log₁₀ 92 / log₁₀ 14 = x
Using a calculator, we can find that log₁₀ 92 = 1.963 and log₁₀ 14 = 1.146. Dividing these two values gives us approximately x = 1.712. Rounding this to the nearest thousandth, we get x ≈ 1.712.