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Write the exponential equation in logarithmic form. e25≈1.2214e^{\frac{2}{5}} \approx 1.2214

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Full solution

Q. Write the exponential equation in logarithmic form. e25≈1.2214e^{\frac{2}{5}} \approx 1.2214
  1. Identify Variables: Identify bb, xx, and yy. Compare e25≈1.2214e^{\frac{2}{5}} \approx 1.2214 with by=xb^y = x. b=eb = e x≈1.2214x \approx 1.2214 y=25y = \frac{2}{5}
  2. Convert to Logarithmic Form: Convert the exponential equation to logarithmic form. Substitute b=eb = e, x≈1.2214x \approx 1.2214, and y=25y = \frac{2}{5} in log⁡b(x)=y\log_b(x) = y. Logarithmic equation: ln⁡(1.2214)≈25\ln(1.2214) \approx \frac{2}{5}
  3. Find Missing Value: Identify the missing value in ln⁡ ____≈25 \ln \, \_\_\_\_ \approx \frac{2}{5} . ln⁡(1.2214)≈25 \ln(1.2214) \approx \frac{2}{5} Missing value: 1.2214 1.2214

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