Answer:
[tex] \displaystyle x = 3.97[/tex]
Step-by-step explanation:
we are given a exponential equation
[tex] \displaystyle {3}^{x} = 78[/tex]
we want to figure out x
remember that,
[tex] \displaystyle \log_{a}( {a}^{c} ) = c[/tex]
thus
take [tex]\log_3[/tex] both sides:
[tex] \displaystyle \log_{3}( {3}^{x} ) = \log_{3}(78) [/tex]
use the formula:
[tex] \displaystyle x = \log_{3}(78) [/tex]
by using calculator
[tex] \displaystyle x = 3.97[/tex]
