# logs

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• #13151

log (3x-5)+log x=3

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• #388

:log (3x-5)+log x=3

2 2

• #13152 Anonymous

Logarithms

A logarithm is a way of representing a number by the power of a base.

i. addition of logs converts to muliplying using this rule clck on image to enlarge

log (3x-5)(x) log (3x^2-5x) . multiply out the brackets

Convert log back to numeric format

click image to enlarge

remember: logaM =x means exactly the same thing as saying a^x = M and log means log10 or log to the base power of 10

becomes

10^3= (3x^2-5x) multiply out the power

1000=(3x^2-5x)

0=3x^2-5x -1000

use -b+-Sqaure root(b^2-4ac)/2a

where a is co-efficient of x^2 (the number with the x^2) ie 3

where b is co-efficient of x (the number with the x]) ie 5

and c is the number without an x term

x=19.12 and -17.44

You should learn the 6 rules relating to logs (they come in useful). I'll post a site if I come across one

Good luck

• #13153 Anonymous
• #13154 Anonymous

Properties of Logarithms Saying that logaM =x means exactly the same thing as saying a^x = M .

the log of the product A*B equals the sum of the logs of A and B

the log of the quotient A/B equals the difference of the logs of A and B.

the log of A to the base a and the power p is equal to p times the log A to the base a

the log of x to the base a is equivilant to the natural log of x divided by the natural log of a. (You would use this rule if you were trying to change the base power)