Question

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

Answer 1

Answer:

x ≈ 2.0794

Step-by-step 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

Answer 2

Answer:

x ≈ 2.0794

Step-by-step 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 )