Can someone help me write 2=3x+1 in exponential form?
Options:
e^2=e^3x+1*
2=e^3x+1
1=e^3x
100=10^3x+1*
The answers with the * both equal 1/3 like the original equation. I don't know if that means anything though:/
Thanks
Which of the following is the equation In 2 = 3x+1 written in exponential form
Is the actual question
the equation ln(2)=3x+1 written in exponential form is 2=e^3x+1
<33
Huh, okay, I see what you mean.
However, I can only choose one answer.
I'm going to go with the first option because I tried working it out on a graph and that option makes more sense.
Thanks for your help
Oh, the joy of math equations! Well, let me try to bring some humor into this.
To write 2=3x+1 in exponential form, I would suggest gathering all the numbers and x on one side and imagine them having a little party. So, let's subtract 1 from both sides to get rid of that pesky party crasher:
2 - 1 = 3x + 1 - 1
That simplifies to:
1 = 3x
Now, we want to make x the center of attention. So, to isolate x, we can divide both sides by 3:
1/3 = (3/3)x
Now, 3 divided by 3 is just 1, so we're left with:
1/3 = x
Voila! We have successfully transformed 2=3x+1 into exponential form, which is "x = 1/3" with a sprinkle of math humor. Keep those equations coming!
To write the equation 2=3x+1 in exponential form, you need to isolate the variable on one side of the equation.
Step 1: Subtract 1 from both sides to isolate the term with the variable.
2 - 1 = 3x + 1 - 1
1 = 3x
Now, let's proceed to rewrite the equation in exponential form.
Exponential form:
To convert the equation 1 = 3x into exponential form, we need to use logarithms.
Step 2: Take the logarithm (base 3) of both sides of the equation. This will allow us to write the equation in terms of an exponent. Since the equation is 1 = 3x, we can write it as:
log3(1) = log3(3x)
Step 3: Simplify the expression using the logarithmic property.
log3(1) is equivalent to 0 since any base raised to the power of 0 equals 1.
0 = log3(3x)
Step 4: Rewrite the equation using the exponential form. In exponential form, the base of the logarithm raised to the power of the result equals the argument. So we have:
3^0 = 3x
Finally, simplify:
1 = 3x
Therefore, the equation 2 = 3x + 1 can be written in exponential form as:
3^0 = 3x
I suspect you have a typo.
2 = 3x + 1 is just a simple equation that has solution of
x = 1/3
x = 1/3 does not satisfy any of the given choices, the way they are written
However, suppose we have:
e^2 = e^(3x+1) ---> 2 = 3x+1
10^2 = 10^(3x+1) ---> 2 = 3x+1
1732.56^2 = 1732.56^(3x+1) ----> 2 = 3x+1
The last eg. is to drive home a point.
Your choices are correct with the insertion of the brackets.