Exponential equations generally have the unknown variable as the power. The
following are examples of exponential equations:
You should already be familiar with exponential notation. Solving exponential
equations is simple, if we remember how to apply the laws of exponentials.
Investigation : solving exponential equations
Solve the following
equations by completing the table:
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
Algebraic solution
Equality for Exponential Functions
If
is a positive number such
that
, (except when
) then:
if and only if:
(If
, then
and
can differ)
This means that if we can write all terms in an equation with the same base, we
can solve the exponential equations by equating the indices. For example takethe equation
. This can be written as:
Since the bases are equal (to 3), we know that the exponents must also be equal.
Therefore we can write:
This gives:
Method: solving exponential equations
Try to write all terms with the same base.
Equate the exponents of the bases of the left and right hand side of the equation.
Solve the equation obtained in the previous step.
Check the solutions
Investigation : exponential numbers
Write the following with the same
base. The base is the first in the list. For example, in the list 2, 4, 8, thebase is two and we can write 4 as
.
2,4,8,16,32,64,128,512,1024
3,9,27,81,243
5,25,125,625
13,169
,
,
,
Solve for
:
All terms are written with the same base.
Since both sides are equal, the answer is correct.
The growth of an algae in a pond can be modeled by the function
. Find the value of
such that
Solve for
:
Solve for
:
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?