Solving Exponential and of
Logarithmic Equations
Page 214
What are the one-to-one properties?
How are they used?
Page 214
What are the inverse properties?
How are they used?
This one is easily solved by just switching to the
exponential form and does not require that
intermediate step.
How are they used?
Just like the last one, this equation is easily solved
by just switching to the exponential form and does
not require that intermediate step.
A different take than the
textbook but the same
conclusion….
A different take than the
textbook but the same
conclusion….
Because Logs are one-to-one functions, we can use the
following formulas to help solve equations…….
1) If M = N, then log b M = log b N
Applying it …..
10 = 257,then log10 = log 257
so, x log10 = log 257
x = log 257
x
x
Because Logs are one-to-one functions, we can use the
following formulas to help solve equations…….
1) If M = N, then log b M = log b N
Applying it …..
Similar problem:
s = 7, since s cannot equal -1
More advanced equations to solve …….
1. Rewrite the equation so you have one log expression on
one side of the equation.
2. Convert the equation to exponential form.
3. Solve the equation.
Applied Problem: Technical Dieting
1. Solve the weight equation for W.
ln(W − W1 ) − ln(W0 − W1 ) = −.005t
⎡ W − W1 ⎤
ln ⎢
⎥ = −.005t
⎣ W0 − W1 ⎦
Now, get the W term on the same side by itself.
ln(W − W1 ) − ln(W0 − W1 ) = −.005t
⎡ W − W1 ⎤
ln ⎢
⎥ = −.005t
⎣ W0 − W1 ⎦
Now, get the W term on the same side by itself.
Solving equations with one exponential expression:
1. Take the Log of each side
2. Use the power rule to get rid of the exponent.
3. Solve for x
(2x − 1)log 4 = log 3
log 3
log 3
2x − 1 =
→ 2x =
+1
log 4
log 4
x=
1 ⎡ log 3 ⎤
+ 1⎥
⎢
2 ⎣ log 4 ⎦
Another equations with one exponential expression:
1. Take the Natural Log of each side
2. Use the power rule to get rid of the exponent.
3. Remember, ln e = 1. Now, Solve for x.
Solve equations with TWO exponential expression:
5
3x − 2
= 3 , solve for x
x
1. Take the Log of each side, and
remove the exponent
2. Distribute terms and get all terms with an x to one side.
Solve equations with TWO exponential expression:
5
3x − 2
= 3 , solve for x
x
3. Factor out x, divide by remaining term.
Let’s look at two other text book examples.
Problems for you ……
From page 221
Vocab 1-3 (all),1-37 odds