use the change of base formula to evaluate log274
To evaluate log274 using the change of base formula, you can use either the natural logarithm (ln) or the common logarithm (log). In this example, let's use the common logarithm.
The change of base formula states:
logᵦa = logc(a) / logc(β)
where a is the value you are taking the logarithm of (in this case 74), β is the base of the original logarithm (in this case 2), and c is the base you want to convert to (in this case 10).
Using the formula, you can compute log274 as:
log274 = log10(74) / log10(2)
Using a scientific calculator or a calculator with built-in logarithm functions, evaluate the expression:
log274 ≈ 6.20905974807
Therefore, log274 ≈ 6.209.