Question

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.

Answer 1

Answer:

The value of log  43is 1.633

Step-by-step explanation:

Explanation:

Suppose you know that:

$\begin{array}{l}{\log 2 \approx 0.30103} \\{\log 3 \approx 0.47712}\end{array}$

Then note that:

$43=\frac{129}{3} \approx \frac{128}{3}=\frac{2^{7}}{3}$

So

$\log 43 \approx \log \left(\frac{2^{7}}{3}\right)=7 \log 2-\log 3 \approx 7 \cdot 0.30103-0.47712=1.63009$

We know that the error is approximately:

$\log \left(\frac{129}{128}\right)=\log 1.0078125=\frac{\ln 1.0078125}{\ln 10} \approx 0.00782 .3=0.0034$

So we can confidently give the approximation:

$\log 43 \approx 1.633$