help with logarithm?

Question

write the logarithm log (a^7/b^3c^4) in terms of log a, log b, and log c.

Answer 1

recall...
log ( x * y ) = log x + log y
log ( x / y) = log x - log y
log ( m^n ) = n log m

use above laws of logarithms
we get
log ( a^7 / b^3 c^4) = log (a^7 ) - log ( b^3 c^4)
= 7 log a - ( log b^3 + log c^4 )
= 7 log a - ( 3 log b + 4 log c )
so final answer is 7 log a - 3 log b - 4 log c

Answer 2

Funny you should ask. First, the rules.
Exponents go outside the log term as multipliers.
Addition of logs corresponds to multiplication of the terms.
Subtraction of logs corresponds to division of the terms.

So...... we have 7log a - (3 log b + 4 log c).
Hope that helps!

Answer 3

Ok, first we must discuss the properties of the logarithm:

First there is the division property, which says:

log(a/b) = loga - logb

Simple.

Then there is the multiplication property, which says:

log(ab) = loga + logb

Finally, there is the exponent property, which says:

log(a^n) = n(loga)

Now we look at your problem:

log(a^7/(b^3c^4))

Division Property:

log(a^7) - log(b^3c^4)

Multiplication Property:

log(a^7) - log(b^3) + log(c^4)

Exponent Property:

7log(a) - 3log(b) + 4log(c)

And there you go.

Answer 4

log(a^7/(b^3c^4) = log(a^7) - log(b^3c^4)
= log(a^7) - log(b^3) - log(c^4)
=7log(a) - 3log(b) - 4log(c)

Answer 5

assuming you mean log[(a^7)/(b^3c^4)]:

apply the properties of logs:
log(xy)= log(x)+ log(y)
log(x/y)= log(x) - log(y)
log(x^y)= ylog(x)

therefore...

log(a^7) - [log(b^3) + log(c^4)]
7log(a) - [3log(b) + 4log(c)] or
7log(a) - 3log(b) - 4log(c)

Answer 6

7loga - 3logb + 4logc

Answer 7

7loga -(3logb + 4logc)

Answer 8

7loga-(3logb+4logc)