Sure, let's solve the log-based equation step-by-step.
Given the equation:
[tex]\[ \log 57.211 = 0.3x - 3.08 \][/tex]
Step 1: Identify the given logarithmic value.
We have:
[tex]\[ \log 57.211 \][/tex]
Step 2: Find the logarithmic value using the base 10.
[tex]\[ \log_{10} 57.211 = 1.757 \][/tex]
(Note: We know this precise value from prior calculations or tables, which is approximately 1.757.)
Step 3: Substitute [tex]\(\log 57.211\)[/tex] in the equation:
[tex]\[ 1.757 = 0.3x - 3.08 \][/tex]
Step 4: Isolate the term containing [tex]\(x\)[/tex]. Add 3.08 to both sides of the equation:
[tex]\[ 1.757 + 3.08 = 0.3x \][/tex]
[tex]\[ 4.837 = 0.3x \][/tex]
Step 5: Solve for [tex]\(x\)[/tex] by dividing both sides by 0.3:
[tex]\[ x = \frac{4.837}{0.3} \][/tex]
[tex]\[ x = 16.1249 \][/tex]
So, the solution to the equation [tex]\(\log 57.211 = 0.3 x - 3.08\)[/tex] yields:
[tex]\[ x \approx 16.125 \][/tex]
Thus, the final answers are:
[tex]\[
\log_{10} 57.211 \approx 1.757
\][/tex]
[tex]\[
x \approx 16.125
\][/tex]
