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7.6 – Solving Exponential
Equations Using Common
Logarithms.
Change of base formula:
The change of base formula allows us to change
any logarithm into base 10.
logb x = log x
log b
Objective: TSW solve exponential equations and
use the change of base formula.
Example: log8 12 =
To evaluate logarithms - Use the
change of base formula to evaluate
logarithms which are not base 10.
Examples:
1. log9 4
2. log8 3
3. 9 – log3 7
Examples:
1. 2x = 49
Solving equations in exponential form:
1. Get the equation in the form “by = x”
2. Rewrite the exponential equation in
logarithmic form (be sure you do not have any
negative numbers within the logarithm)
3. Use the change of base formula to evaluate the
logarithm.
4. Solve for x.
Examples:
2. 8x = 240
3. 2x+1 = 30
4. 67 –2-x = 39
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Examples:
5. 5x +12= 67
6. 15x^2 = 110
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