explain the solving of equationexplain how to deal with an exponential equation where bases are not the same. a^x=b

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

To solve an equation of the form a^x = b where the bases are not the same we cannot equate the exponents.

Instead logarithms can be used

log a^x = log b

use the property log a^x = x*log a

=> x*log a = log b

=> x = log b / log a

The solution of these kind of equations is log b/ log a

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

One example:

3^(x-3)=17

To determine x, we'll take log on both sides:

log 3^(x-3)=log 17

We'll use the power rule of logarithms:

(x-3)*log 3 = log 17

We'll divide by log 3 both sides of the equation:

(x-3) = log 17 / log 3

We'll add 3  both sides:

x = log 17 / log 3 + 3

We'll compute the ratio log 17 / log 3 + 3:

log 17 / log 3 = 1.2304/0.4771 + 3

x = 2.6617/0.4771

x = 5.5789 approx.

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frontman0 | Student, Undergraduate | (Level 1) Honors

Posted on

provide a practical example of such a problem

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