Pregunta
What is the true solution to the logarithmic equation below?
Ask by Bolton Marsh. in the United States
Dec 14,2024
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Responder
The true solution is
.
Solución

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Como
The Deep Dive
To solve the equation
, we can start by rewriting the equation. Remember that
implies that
. Thus, we have:
Now, rewriting
means that
. Calculating
:
Therefore, we get:
Dividing both sides by 2 gives us:
So, the true solution to the logarithmic equation is
.
Now, let’s delve into some additional background on logarithmic equations and their applications.
Did you know that logarithmic scales are used in many fields? For example, the Richter scale measures earthquake intensity, and the decibel scale quantifies sound intensity. These scales use logarithms because they allow us to represent and compare huge ranges of values in practical, manageable terms.
Another interesting aspect is how people often confuse the base of a logarithm. A common mistake is misreading the equation, like thinking
directly without considering the base. Always make sure to keep track of the base when solving logarithmic equations; it can change the entire problem!

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