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aisha
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I got x=1.4335735 off of my graphing calculator, but is it possible to solve without a graphing calculator?
Jameson said:using logs.
(2x+1)ln3 = ln70
Jameson said:i'm pretty sure that's the only way. logs are just another way of expressing radicals. But I won't go into detail.
If you solve that equation, you get 2x + 1 = ln70 / ln 3
so the answer is actually 2.43. that's what i get at least
Gecko said:i don't get how you got and used the inequality 70<81. couldn't you use the logarithim rule that states logx y= log a y/ log a x so then you would get 2x+1 = log 70/ log 3 which should give you the same answer as what jameson got, if he is correct.
edit: jameson was wrong, i did the calculations and got 1.433573512... which is what the person who asked the question got when he/she put it into a graphing calculator.
To solve this equation without a graphing calculator, you can use logarithms. First, take the logarithm of both sides of the equation. This will give you log(3^(2x+1))=log(70). Then, you can use the power rule of logarithms to bring down the exponent, giving you (2x+1)log(3)=log(70). From there, you can isolate the variable by dividing both sides by log(3). This will give you 2x+1=log(70)/log(3). Finally, you can solve for x by subtracting 1 and then dividing by 2, giving you x=(log(70)/log(3)-1)/2.
It is important to know how to solve equations without a graphing calculator because not all equations can be solved using a calculator. Additionally, understanding the concepts and steps involved in solving equations by hand can help develop problem-solving skills and a deeper understanding of mathematical concepts.
Yes, you can use a scientific calculator to solve this equation. However, keep in mind that not all scientific calculators have a logarithm function. If your calculator does not have a logarithm function, you will not be able to solve this equation using it.
Yes, there are other methods for solving this equation without a graphing calculator. One method is to use trial and error, plugging in different values for x until you find the solution. Another method is to rewrite the equation in a different form, such as writing 70 as a power of 3, and then using properties of exponents to solve for x.
Yes, you can check your answer by plugging it back into the original equation and seeing if it satisfies the equation. For example, if your solution is x=2, you can plug in 2 for x in the equation 3^(2x+1)=70 to see if it equals 70. If it does, then your solution is correct. You can also use a scientific calculator to check your solution by plugging in the value of x and seeing if the left and right sides of the equation are equal.