Question

Solve each equation. Round to four decimal places.
e^x=8

Answer 1

x ≈ 2.0794

Explanation:

Given

`e^(x)` = 8 ( take ln of both sides )

ln
`e^(x)` = ln 8

x lne = ln 8 [ lne = 1 ]

x = ln 8 ≈ 2.0794 ( to 4 dec. places )

Answer 2

x ≈ 2.0794

Explanation:

`\small \sf \: e {}^(x) = 8`

Take the natural logarithm of both side of equation

• 
  `\small \sf \: In ( e {}^(x) ) = In ( 8 )`

`\small \sf \: Use \: In(e {}^(x) ) = x \: to \: simplify \: the \: expression.`

• x = In( 8 )

Write the number in exponential form.

• x = In(2³)

Use In(aⁿ) = n × In ( a ) to transform the expression.

• x = 3In( 2 ) ≈ 2.07944

Round to four decimal places = 2.0794