Large-exponent.py

[lucentlabz]

import math

Given values

base = 0.123456789
exponent = 987654321.0

Step 1: Calculate the natural logarithm of the base

ln_base = math.log(base)

Step 2: Multiply by the exponent

power_term = exponent * ln_base

Step 3: Exponentiate the result

result = math.exp(power_term)

Output the result

print(f"The approximate value of {base}^{exponent} is {result:()}")

[lucentlabz]

import math

Given values

base = 0.123456789
exponent = 987654321.0

Step 1: Calculate the natural logarithm of the base

ln_base = math.log(base)

Step 2: Multiply by the exponent

power_term = exponent * ln_base

Step 3: Exponentiate the result

result = math.exp(power_term)

Output the result

print(f"The approximate value of {base}^{exponent} is {result:.2e}")

[lucentlabz]

Here's the correct Python code to compute (0.123456789^{987654321.0}) using logarithmic properties:

import math

# Given values
base = 0.123456789
exponent = 987654321.0

# Step 1: Calculate the natural logarithm of the base
ln_base = math.log(base)

# Step 2: Multiply by the exponent
power_term = exponent * ln_base

# Step 3: Exponentiate the result
result = math.exp(power_term)

# Output the result
print(f"The approximate value of {base}^{exponent} is {result:.2e}")

Explanation:

1. Calculate the natural logarithm:
   [ \ln(\text{base}) ]
2. Multiply by the exponent:
   [ \text{power_term} = \text{exponent} \times \ln(\text{base}) ]
3. Exponentiate the result:
   [ \text{result} = e^{\text{power_term}} ]

This approach ensures numerical stability for extremely large or small results.