The greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.
The given logarithmic expression is log(1.3 x 10⁷)
Use the product rule of the logarithm logₐ(X.Y) = logₐ(X) + logₐ(Y), to get
log(1.3 x 10⁷)
= log(1.3) + log(10⁷)
= log(1.3) + 7 log(10) (Using the power rule of the logarithm logₐ(Xⁿ) = n logₐ(X))
= log(1.3) + 7 (Since log(10) = 1)
≈ 7.113 (approximate value)
We know that, log(1) = 0 and log(10) =1. And the logarithm is an increasing function.
So, log(1.3) is very close to 0 and strictly less than 1.
Therefore, the greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.
Learn more about logarithm at:
https://brainly.com/question/2516397
#SPJ4
