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Chapter 26: Problem 775

Find Antilog \(_{10} 0.8762-2\).

Short Answer

Expert verified
The short answer is: \(\text{Antilog}_{10} (0.8762 - 2) = 0.076\).

Step by step solution

01

Understand the Term Given

The problem has given us an anti-logarithm to calculate. This term is \(\text{Antilog} _{10} (0.8762 -2)\). Here, the base of the anti-log is 10 and the number inside the brackets is \(0.8762-2\), which needs to be solved first.
02

Simplify Inside the Brackets

Before proceeding with the anti-logarithm, simplify the expression inside the brackets. \(0.8762 - 2 = -1.1238\). So, the anti-logarithm becomes \(\text{Antilog} _{10} (-1.1238)\).
03

Compute the Anti-logarithm

Now, the aim is to find the anti-logarithm of -1.1238 (base 10). For this, we use the formula \(\text{antilog}_ {10} (x) = 10^x\). Substituting the value of x as -1.1238, the equation becomes \(\text{Antilog}_{10} (-1.1238) = 10^{-1.1238}\).
04

Compute the Exponential Term

Most calculators have a button to compute 10 raised to the power of any given number. Use this feature to solve \(10^{-1.1238}\), which comes out to be approximately 0.076. So, \(\text{Antilog}_{10} (0.8762 - 2) = 0.076\).

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