How to Calculate -log(2.9 x 10^-5): Step-by-Step Guide

To calculate the logarithm, we can use the natural logarithm function (ln) or the common logarithm function (log base 10), as both will give the same result.

Using the natural logarithm (ln): -ln(2.9 * 10^-5) = -ln(2.9) - ln(10^-5)

Since ln(10^-5) = -5 * ln(10) and ln(10) ≈ 2.30259, we can substitute this value: -ln(2.9 * 10^-5) = -ln(2.9) - (-5 * ln(10)) ≈ -ln(2.9) + 5 * ln(10)

Now, we need to calculate the values of ln(2.9) and ln(10).

Using a scientific calculator or math tool: ln(2.9) ≈ 1.06471 ln(10) ≈ 2.30259 (as mentioned earlier)

Substituting these values back into the equation: -ln(2.9 * 10^-5) ≈ -1.06471 + 5 * 2.30259

Simplifying further: -ln(2.9 * 10^-5) ≈ -1.06471 + 11.51295 ≈ 10.44824

Therefore, -log(2.9 * 10^-5) ≈ 10.44824.