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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!
given log a 2= 1.8301 and log a 7= 5.0999
what is log a 3.5=?
Thanks!
benjyk said:This may come in handy..
log(a/b)=log(a)-log(b)
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.
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.
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.
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.
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".