9514 1404 393
Answer:
(1) logb(d/a) +c
Step-by-step explanation:
As with any "solve for ..." problem, it is useful to consider the operations performed on the variable. The Order of Operations helps you here.
For this equation, we have ...
- c is subtracted from x
- b is raised to that power
- a multiplies the result.
The way to proceed is to "undo" these operations, starting from the last one and working up the list.
We undo multiplication using division. Here, we need to divide by a.
[tex]b^{x-c}=\dfrac{d}{a}[/tex]
We can unto the raising to a power by using logarithms. Here, it is convenient to use base-b logarithms.
[tex]x-c=\log_b{\left(\dfrac{d}{a}\right)}[/tex]
Finally, we undo the subtraction of c by adding it to the equation.
[tex]\boxed{x=\log_b{\left(\dfrac{d}{a}\right)}+c}\qquad\textbf{matches (1)}[/tex]
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The applicable rule is that these two expressions are equivalent:
[tex]b^x=y\quad\leftrightarrow\quad x=\log_b(y)[/tex]
