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


Sagot :

Answer:

x ≈ 2.0794

Step-by-step explanation:

Given

[tex]e^{x}[/tex] = 8 ( take ln of both sides )

ln [tex]e^{x}[/tex] = ln 8

x lne = ln 8 [ lne = 1 ]

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

Answer:

x ≈ 2.0794

Step-by-step explanation:

[tex] \small \sf \: e {}^{x} = 8[/tex]

Take the natural logarithm of both side of equation

  • [tex]\small \sf \: In ( e {}^{x} ) = In ( 8 )[/tex]

[tex] \small \sf \: Use \: In(e {}^{x} ) = x \: to \: simplify \: the \: expression.[/tex]

  • 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