Enter the base and result value to quickly find the missing exponent.
If the base and the result value are known, logarithms can be used to determine the missing exponent. Follow these steps:
Solution:
Given: Base \( a = 2 \), Result \( V = 32 \).
Calculation:
Using the formula: \( n = \log_2 32 \)
Convert to common logarithms:
\( n = \frac{\log 32}{\log 2} \)
Compute values:
\( \frac{\log 32}{\log 2} = \frac{1.505}{0.301} = 5 \)
Result: The missing exponent is 5, meaning \( 2^5 = 32 \).
Solution:
Given: Base \( a = 3 \), Result \( V = 81 \).
Using the formula:
\( n = \log_3 81 \)
Convert to common logarithms:
\( n = \frac{\log 81}{\log 3} \)
Compute values:
\( \frac{\log 81}{\log 3} = \frac{1.908}{0.477} = 4 \)
Result: The missing exponent is 4, meaning \( 3^4 = 81 \).
Solution:
Given: Base \( a = 5 \), Result \( V = 125 \).
Using the formula:
\( n = \log_5 125 \)
Convert to common logarithms:
\( n = \frac{\log 125}{\log 5} \)
Compute values:
\( \frac{\log 125}{\log 5} = \frac{2.096}{0.699} = 3 \)
Result: The missing exponent is 3, meaning \( 5^3 = 125 \).