Take the logarithm of both sides. The base of the logarithm doesn't matter.


Drop the exponents:

Expand the right side:

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :


Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

You can stop there, or continue simplifying the solution by using properties of logarithms:



You can condense the solution further using the change-of-base identity,

If the CAT operates with a constant speed of 53 mph (which means it beats 53 miles in one hour) and makes a trip in about 2 and 1/2 hours, we just have to multiply 53 by 2 1/2 to find out the overall distance it's beating in that time:
53 * 2 1/2 =
= 53 * 2.5 =
= 132.5
Answer: City A is about <u>132.5 miles</u> from city B.
Since z is proportion to the x
z = a x
190 = a 10
a = 19
when x = 13
z = a x
z = 19 * 13
z = 247