To calculate logarithm without a calculator, you can use the concept of approximation using a series expansion or logarithm tables.
The series expansion of the natural logarithm (ln) behaves similarly to the logarithm (log) with different bases. You can use the following series expansion for calculating ln:
ln(1 + x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + (x^5)/5 - ...
Using this series expansion, you can approximate log(1.05) by substituting x = 0.05 (since log(1.05) is the same as ln(1.05)), and stop the expansion after a certain number of terms to get an approximate value.
ln(1.05) ≈ 0.05 - (0.05^2)/2 + (0.05^3)/3 - (0.05^4)/4 + (0.05^5)/5
Calculating this expression manually will give you an approximation of log(1.05) without using a calculator.
how to calculator log without using a calcator?
log(1.05) 10
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