How do you solve #-5*10^(3b)=-77#?

1 Answer
Sep 5, 2016

Answer:

#b = (1) / (3) (log(77) - log(5))#

Explanation:

We have: #- 5 cdot 10^(3 b) = - 77#

Let's begin by dividing both sides of the equation by #- 5#:

#=> 10^(3 b) = (77) / (5)#

Then, let's apply logarithms to both sides:

#=> log(10^(3 b)) = log((77) / (5))#

Now, using the laws of logarithms:

#=> 3 b log(10) = log(77) - log(5)#

#=> 3 b = log(77) - log(5)#

#=> b = (1) / (3) (log(77) - log(5))#