Help with Logs!

I'm stuck doing logs homework, hope someone can help.

The variables x and y are connected by a relationship of the form y=ax^n, where a and n are constants.
Show that there is a linear relationship between log10y and log10x.

Help! Log10y means log(small 10)y :smile:

Reply 1

hello calum

10

Original post by BethArkless

I'm stuck doing logs homework, hope someone can help.

The variables x and y are connected by a relationship of the form y=ax^n, where a and n are constants.
Show that there is a linear relationship between log10y and log10x.

Help! Log10y means log(small 10)y :smile:

try taking logs of both sides. and remember that

log(AB) = log(A) + log(B)

and

log(A^B) = Blog(A)

edit: and remember that a linear relationship is one of the form

y = mx + c

(edited 11 years ago)

Reply 2

BethArkless

OP

But the two logs aren't adding or multiplying ?

Reply 3

TenOfThem

18

Original post by BethArkless

But the two logs aren't adding or multiplying ?

What two logs

As was said

Take logs of both sides

Reply 4

Mark85

16

Original post by BethArkless

I'm stuck doing logs homework, hope someone can help.

The variables x and y are connected by a relationship of the form y=ax^n, where a and n are constants.
Show that there is a linear relationship between log10y and log10x.

Help! Log10y means log(small 10)y :smile:

You want to show that

\log_{10}(y) = b\log_{10}(x)+c

for some numbers

b,c

(this is the definition of linear relationship).

Now, if

y=ax^n

then

\log_{10}(y) = \log_{10}(ax^n)

Now use the basic log laws (in two steps if necessary) to expand the right hand side until you get something of the required form above.

Help with Logs!

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