Math Is Fun Forum

makar92

Member

Registered: 2008-08-10

Posts: 6

hard problems for swedish mathematics c

1) find all solutions to the equation:

x^(lg_x)=(x^(3/100))

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2) what do you get when solving the equation:

nDeriv(a^x, x, 1)=a
with attention to a?

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3) how do we derive i.e. y=7^x? the answer is that we change the base e this way:

if 7=e^z, then z=log_e(7) ⇒ 7=e^(log_e(7))

this is the only example in the book and i can't understand the method. please explain a little simplier.

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these three problems i really need help with.
if you don't understand the question please let me know 'cause i'm not a native english speaker.

ps: i have the answer to the first 2 problems, but i need to understand every step into detail.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: hard problems for swedish mathematics c

for number 1

for number 3

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makar92

Member

Registered: 2008-08-10

Posts: 6

Re: hard problems for swedish mathematics c

okay thx.. if anyone could help me with the second problem that would be awesome. a should be e and i see why because k=1 but i still can't understand how to solve it.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: hard problems for swedish mathematics c

what do you mean by nDeriv? do you mean the n'th derivitve? i.e.

then what is the third value in the brackets for?

Last edited by luca-deltodesco (2008-08-11 03:23:58)

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makar92

Member

Registered: 2008-08-10

Posts: 6

Re: hard problems for swedish mathematics c

nDeriv is on my calculator, when we want the calculator to derive.

here is translated what is standing in the answer:

if y=a^x, then you get the base a that is such as y'(1)=a
Solve (nDeriv(a^x, x, 1) -a, a, 2) gives a≈2,718

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: hard problems for swedish mathematics c

ah i see.

x = 1 hence

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