Help with LOGs and E please!

kmarkwell

New member
Joined
Apr 9, 2007
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2
I need a little help understanding how to solve these problems.

1) Solve: LOGv4(64)

2) Solve for x: 4e^(4x-1)=2.1

How do I solve for x when x is an exponent?

3) Solve for x: 10^(2x-1)=e^(4x-3)

4) Solve for x: xLOG(43)=7+e^1.9

I might have this one: I got 8.40...?

Thank You!
 
kmarkwell said:
1) Solve: LOGv4(64)
There is no equation here to solve; you have posted only an expression. If this is supposed to be an equation, please post the "equals" and whatever was on the other side. Otherwise, please post the actual instructions. For instance, were you supposed to "evaluate for the given value of the variable 'v'", or something else?

kmarkwell said:
2) Solve for x: 4e^(4x-1)=2.1

How do I solve for x when x is an exponent?
You would take logs of either side of the equation (after dividing through by 4, of course). Then apply log rules (you should have a list of them in your book and/or your class notes) to get the x by itself.

kmarkwell said:
3) Solve for x: 10^(2x-1)=e^(4x-3)
Take logs. I would suggest either the common log or the natural log. Either way, the answer is going to be messy....

kmarkwell said:
4) Solve for x: xLOG(43)=7+e^1.9

I might have this one: I got 8.40...?
You can check the answer to any "solving" problem by plugging your answer back into the original exercise. In this case:

. . .left-hand side:
. . . . .x log(43) = (8.4) log(43) = 13.72 (approx.)

. . .right-hand side:
. . . . .7 + e<sup>1.9</sup> = 13.69 (approx.)

Allowing for round-off error, your solution is probably correct. But your instructor will probably want the answer in "exact" form, so be sure to include this, along with your decimal approximation.

Eliz.
 
kmarkwell said:
I need a little help understanding how to solve these problems.

1) Solve: LOGv4(64)

hint ... 4<sup>3</sup> = 64

2) Solve for x: 4e^(4x-1)=2.1

How do I solve for x when x is an exponent? by using logarithms

4e<sup>4x-1</sup> = 2.1
divide both sides by 4 ...
e<sup>4x-1</sup> = 2.1/4
take the natural log of both sides ...
ln(e<sup>4x-1</sup>) = ln(2.1/4)
4x-1 = ln(2.1/4)

finish up and solve for x.



3) Solve for x: 10^(2x-1)=e^(4x-3)

take the natural log of both sides ...
ln(10<sup>2x-1</sup>) = ln(e<sup>4x-3</sup>)
(2x-1)ln(10) = 4x-3
2ln(10)*x - ln(10) = 4x - 3
2ln(10)*x - 4x = ln(10) - 3
x[2ln(10) - 4] = ln(10) - 3
x = [ln(10) - 3]/[2ln(10) - 4]


4) Solve for x: xLOG(43)=7+e^1.9

I might have this one: I got 8.40...?

close ... x = (7 + e<sup>1.9</sup>)/log(43) = 8.378...

Thank You!
 
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