Solving Exponential Equations with Logarithms
Algebra · Flashcards · Recall
ALGEBRA · FLASHCARDS
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QUESTION
Identify the final step to isolate
t
t
t
from
c
t
=
log
b
(
d
a
)
ct=\log_b\left(\frac{d}{a}\right)
c
t
=
lo
g
b
(
a
d
)
.
QUESTION
State the change-of-base formula for rewriting
log
b
(
x
)
\log_b(x)
lo
g
b
(
x
)
using
log
\log
lo
g
.
QUESTION
Rewrite the solution of
a
⋅
10
c
t
=
d
a\cdot 10^{ct}=d
a
⋅
1
0
c
t
=
d
using
ln
\ln
ln
only.
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ANSWER
t
=
ln
(
d
a
)
c
ln
(
10
)
t=\frac{\ln\left(\frac{d}{a}\right)}{c\ln(10)}
t
=
c
l
n
(
10
)
l
n
(
a
d
)
. Apply change-of-base formula:
log
10
(
x
)
=
ln
(
x
)
ln
(
10
)
\log_{10}(x) = \frac{\ln(x)}{\ln(10)}
lo
g
10
(
x
)
=
l
n
(
10
)
l
n
(
x
)
.
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