Write the expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).
= 1
To write the expression in terms of common logarithms, we can use the relationship between common logarithms (base 10) and natural logarithms (base e).
The conversion formula is: log_a (x) = ln(x) / ln(a)
In this case, we want to express the expression in terms of common logarithms, which means we need to find a value for "a". Since the common logarithm is base 10, we can rewrite the expression as:
log_10 (1)
Now, we can use the conversion formula with "a = 10":
log_10 (1) = ln(1) / ln(10)
The natural logarithm of 1 is 0, and the natural logarithm of 10 is approximately 2.3026 (you can use a calculator to find this value).
Therefore, the expression in terms of common logarithms is:
log_10 (1) ≈ 0 / 2.3026
Now, let's calculate the approximation using a calculator:
log_10 (1) ≈ 0
So, the calculator approximation of the expression is 0.0000 (correct to four decimal places).