Answer: The value of [tex]n[/tex] is 5
Step-by-step explanation:
-Solve:
[tex]3^2[/tex] × [tex]3^3[/tex] [tex]=3^n[/tex]
-If two numbers with exponents are multiplying together, then the exponents would add up together:
[tex]3^5 = 3^n[/tex]
-Simplify by the exponent:
[tex]243 = 3^n[/tex]
-Take the logarithm both sides of the equation:
[tex]log(3^n)= log (243)[/tex]
- Then, you divide both sides by [tex]log (3)[/tex] :
[tex]n=\frac{log(243)}{log(3)}[/tex]
- Use the change-of-base formula, which is [tex]\frac{log(a)}{log(b)} = log_{b}(a)[/tex]:
[tex]n = log_{3}(243)[/tex]
[tex]n = 5[/tex]
So, the value of [tex]n[/tex] is 5.
