Log a 3.5: Finding the Solution using Logarithmic Rules

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In summary, the value of "a" in the equation Log a 3.5 can be found by solving for it with a base of 10, resulting in a value of approximately 0.544068. It can also be solved without a calculator using logarithm properties and algebraic manipulation. The solution represents the exponent of the power that results in 3.5, and can be checked using various methods. The equation can have multiple solutions, but the most simplified and commonly considered solution is the positive value of "a".
  • #1
JasonX
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[SOLVED] log a 3.5= ?

given log a 2= 1.8301 and log a 7= 5.0999

what is log a 3.5=?

Thanks!
 
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  • #2
Why does the thread name say solved?

Anyway, Please show us some working, we can't help you otherwise. All I'm going to say is to remember some log identities. You must see a relation between 3.5, 7 and 2.
 
  • #3
This may come in handy..

log(a/b)=log(a)-log(b)
 
  • #4
benjyk said:
This may come in handy..

log(a/b)=log(a)-log(b)

*sigh* Well stuff the forum regulations hey?
 

1. What is the value of "a" in the equation Log a 3.5=?

The value of "a" can be found by solving for it in the equation. In this case, since the base of the logarithm is not specified, we can assume it is the common logarithm with a base of 10. Therefore, the equation becomes 10^x = 3.5, where x is the value of "a". Using a calculator or by trial and error, we can find that a is approximately 0.544068.

2. Can the equation Log a 3.5= be solved without a calculator?

Yes, the equation can be solved without a calculator by using logarithm properties and algebraic manipulation. For example, we can rewrite the equation as 10^x = 3.5 and then take the logarithm of both sides using the base 10. This will result in x = log 3.5, which can then be evaluated using logarithm tables or by using the change of base formula.

3. What is the significance of the solution to Log a 3.5=?

The solution to the equation represents the power to which the base (in this case, 10) must be raised to equal 3.5. In other words, it is the exponent of the power that results in 3.5. This is useful in many applications, such as calculating pH levels in chemistry or determining the decibel level in sound engineering.

4. Is there a way to check if the solution to Log a 3.5= is correct?

Yes, there are various ways to check if the solution is correct. One way is to substitute the value of "a" into the original equation and see if it results in 3.5. Another way is to graph the equation and see if the point (a, 3.5) lies on the graph. Additionally, we can use logarithm properties to simplify the equation and see if the simplified form is equivalent to the original equation.

5. Can the equation Log a 3.5= have more than one solution?

Yes, the equation can have more than one solution. This is because logarithms are not one-to-one functions, meaning that different inputs can result in the same output. In this case, the equation can have an infinite number of solutions, as any value of "a" that results in 10^x = 3.5 is a valid solution. However, we usually only consider the most simplified solution, which is the positive value of "a".

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