Respuesta :
Answer:
6.66
Step-by-step explanation:
First, you must convert the equation [tex]3^w=1509[/tex]
In order to change exponents to logarithmic functions, you can follow the rule that [tex]a^b = c[/tex] is the same as [tex]log_a(c)=b[/tex]
Personally, I like to think of it like a circular half arrow. The arrow starts on a, circles to c, and ends on b which means the order will be a, c, and b; then you simply put the order into the log function as log a(since it's first) c (second) = b(third)
Following the rule above, converting [tex]3^w=1509[/tex] turns into [tex]log_3(1509) = w[/tex].
Solve for w using change of base formula which states [tex]log_a(b) = \frac{log_x(b)}{log_x(a)}[/tex]
Let x be 10, so you can input the equation into your calculator to solve.
log3(1509) = (log10(1509))/(log10(3)) = [tex]\frac{log1509}{log3}[/tex] or [tex]\frac{ln1509}{ln3}[/tex] = 6.66222 = 6.66
