Solving Logs 3
The third of 4 skills relating to logarithms requires using logs
since they cannot be re-expressed with the same base.
Bases are NOT equal and can not be re-expressed.
If 5x = 9y and since 5 & 9 cannot be re-expressed withthe same base, logs must be used.
In oher words in this case: x ≠ y
The solution starts
like this
Solving Exponential Equations
5x = 9y
log5x = log9y
x•log5 = y•log9
take log of both sides
bring power down
Example #1:
log15x = log94x•log15 = log94x•1.176 = 1.973
x = 1.68
1.176
1.176
Solving Exponential Equations
take log of both sides
bring power down
estimate logs in your calculator
use algebra to solve for x
Example #2:
14m-8 + 2 = 100           - 2      - 2
14m-8 = 98log14m-8 = log98(m-8)•log14 = log98(m-8)•(1.146) = 1.991
Solving Exponential Equations
use algebra to isolatethe exponential
take log of both sides
bring power down
estimate logs in your calculator
use algebra to solve for x
(m-8)•(1.146) = 1.991
1.146
m - 8 = 1.74
    + 8   + 8
m = 9.74
1.146
Solve for b.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for x.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for x.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for p.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for x.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for n.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for m.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for n.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for n.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
Solve for v.
Answer: Round to hundredths             (ie. 2.34 or 0.63 or -2.00)
Solving Exponential Equations
use algebra to isolate exponentialtake logs of both sidesbring power downestimate logsuse algebra to solve
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