Answer:
x = 4 + (log 6 / log 3)
x ≈ 5.631
Step-by-step explanation:
3^(x − 4) = 6
Take log base 3 of both sides.
log₃ 3^(x − 4) = log₃ 6
x − 4 = log₃ 6
Use change of base formula.
x − 4 = log 6 / log 3
Solve for x.
x = 4 + (log 6 / log 3)
x ≈ 5.631
Answer:
5.631
Step-by-step explanation:
Using the change of base formula log base b of y equals log y over log b
Log y (base b) = log y /log b
3^(x − 4) = 6
Taking the log of both sides
log 3^(x − 4) = log 6
using the logarithm law that states that
log a ^ x = x log a
x - 4 log 3 = log 6
x - 4 = log 6 / log 3
x - 4 = 1.630929754
x = 5.630929754
≈ 5.631
