SOLVING EXPONENTIAL EQUATIONS USING LOGARITHMS

The logarithm (or simply, log) of a positive number is its power of 10.

This means that any positive number a can be written in base 10 as a = 10log a.

Solve for x using logarithms:

Problem 1 :

2x = 100

Solution :

2x=10010log 2x=102x×log 2 = 2x = 2log 2x = 20.301x=6.644

Problem 2 :

(1.12)x = 3

Solution :

(1.12)x=310log 1.12x=10log 3x×log 1.12 = log 3x = log 3log 1.12x = 0.4770.049x=9.694

Problem 3 :

2x = 3

Solution:

2x=310log 2x=10log 3x×log 2 = log 3x = log 3log 2x = 0.47710.3010x=1.585

Problem 4 :

2x = 10

Solution:

2x=1010log 2x=10log 10x×log 2 = log 10x = log 10log 2x = 10.3010x=3.322

Problem 5 :

2x = 400

Solution:

2x=40010log 2x=10log 400x×log 2 = log 400x = log 400log 2x = 2.6020.3010x=8.644

Problem 6 :

2x = 0.0075

Solution:

2x=0.007510log 2x=10log 0.0075x×log 2 = log 0.0075x = log 0.0075log 2x = -2.12490.3010x=-7.059

Problem 7 :

5x = 1000

Solution:

5x=100010log 5x=103x×log 5 = 3x = 3log 5x = 30.6989x=4.292

Problem 8 :

6x = 0.836

Solution:

6x=0.83610log 6x=10log 0.836x×log 6 = log 0.836x = log 0.836log 6x = -0.0770.7781x=-0.09997

Problem 9 :

(1.1)x = 1.86

Solution:

(1.1)x=1.8610log 1.1x=10log 1.86x×log 1.1 = log 1.86x = log 1.86log 1.1x = 0.26950.0413x=6.511

Problem 10 :

(1.25)x = 3

Solution:

(1.25)x=310log 1.25x=10log 3x×log 1.25 = log 3x = log 3log 1.25x = 0.47710.0969x=4.923

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