Answered: You must isolate the base and exponent…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.6: Exponential And Logarithmic Equations

Problem 79SE: Recall the formula for continually compoundinginterest, y=Aekt. Use the definition of a...

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You must isolate the base and exponent expression before converting.
• Use properties to isolate the base/variable expression;
• Convert the equation from exponential form to log form;
• Evaluate the logarithm using the change of base formula and your calculator

(k)(m^x ) + p = q (w)(r^x ) – s = t

Expert Solution

Step 1

Given- $(k) (m^{x}) + p = q$

To find- The expression of the above expression in terms of variable using logarithm function.

Identity Used- $\log (m \cdot n) = \log m + \log n, \log (\frac{m}{n}) = \log m - \log n and \log a^{m} = m \log a$

Step 2

Explanation- Rewrite the given expression,

$(k) (m^{x}) + p = q$

Simplifying the above expression, we get,

$(k) (m^{x}) = q - p$

Now, taking log both sides, we get,

$\log_{10} (k \cdot m^{x}) = \log_{10} q$

Now, using the formula $\log (m \cdot n) = \log m + \log n$ , we get,

$\log_{10} k + \log_{10} m^{x} = \log_{10} q \log_{10} k + x \log_{10} m = \log_{10} q$

As we have ti isolate the variable from the expression, which is as follows,

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