Julio and Kyle hike along the same trail. Kyle hikes the first 6 miles in 2 hours. Who hikes more quickly?
Julio hikes the first 1/2 mile of the trail in 1/4 hour.

Julio hikes more quickly.

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: