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

Asked on by frontman0

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 | 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.

frontman0 | Student, Undergraduate | (Level 1) Honors

Posted on

provide a practical example of such a problem
The text passage contains multiple explanations of how to solve exponential equations where the bases are not the same. It includes a general method and a specific example with a solution.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# explain the solving of equationexplain how to deal with an exponential equation where bases are not the same. a^x=b

Asked on by frontman0

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 | 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.

frontman0 | Student, Undergraduate | (Level 1) Honors

Posted on

provide a practical example of such a problem
user
The text passage contains multiple explanations of how to solve exponential equations where the bases are not the same. It includes a general method and a specific example with a solution.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS