Question

Use a calculator to find an approximate solution to the equation. Round any intermediate work and steps to three decimal places. Show all of your steps.
7ln (x + 2.8) = 11.2

Answer 1

ln(x +2.8) = 11.2/7n= 1.6
ln 4 = 1.386
ln 5 = 1.609

so x + 2.8 is close to but below 5

Answer 2

i suggest you start at 4.9 and plug in values 4.91, 4.92 etc to get a root to 2 decimals; - then sub in 3 decimal place values to finally get a root correct to 2 decimal places

Answer 3

try 4.92 : x-2.8 = ln 4.92 = 1.5933
try 2.94 x - 2.8 = ln 4.94 = 1.5973
try 4.96 = 1.6014


- looks like root is about 4.95

try 4.945 = 1.5983 - a little low
4.95 = 1.59938 - very close
4.955 = 1.6004

- this is higher tha 1.6
so the answer is 4.95 correct to 2 decimal places

oh we need to subtract 2.8

root = 4.95-2.8 = 2.15 to 2 DP's

Answer 4

the correct answer to 3 decimal places is 2.153

Answer 5

\(\Huge\frak\color{magenta}{Thank~You!}\)