Answer: log 10 is approximately 1.2552.
Explanation:
To evaluate the logarithm log 10 using the given values of log 102 and log 109, we can use the property of logarithms that states:
log a (x * y) = log a (x) + log a (y)
Since we know that 10 can be expressed as the product of 102 and 109:
10 = 102 * 109
We can rewrite the logarithmic equation as:
log 10 = log (102 * 109)
Applying the property of logarithms mentioned earlier:
log 10 = log 102 + log 109
Substituting the given values:
log 10 ≈ 0.3010 + 0.9542
Calculating the sum:
log 10 ≈ 1.2552
Therefore, using the given values of log 102 and log 109, the value of log 10 is approximately 1.2552.