Question 947737: Use logarithms to solve the given equation. (Round the answer to four decimal places.) 7^−4x = 45 Found 2 solutions by Theo, MathLover1:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! start with 7^(-4x) = 45
take the log of both sides of this equation to get:
log(7^(-4x)) = log(45)
this becomes -4x*log(7) = log(45)
divide both sides of this equation by log(7) to get:
-4x = log(45) / log(7)
divide both sides of this equation by -4 to get:
x = log(45) / (log(7) / -4
solve for x to get x = -.4890593859
confirm by replacing x in the original equation to get:
7^(-4*-.4890593859) = 45
simplify to get 45 = 45.
this confirms the solution is correct.
