log question?

Question

How can I use my calculator to solve a log?

For example:

log[base 3] 9^2

Answer 1

I will write log [base 10] as lg

log[base 3] (9^2)
=lg(9^2) / lg 3
= 4

Answer 2

In the following , log means log to base 3:-
log 9² = 2.log 9= 2.log 3² = 4.log 3 = 4

Answer 3

Late on your homework eh?

Well, we'll start with the calculator, but you should understand the basics also.

Well, in the chapter on logs that you are working on, you'll note two rules: The property of logarithms where you can pull the exponent in front of the log

2*log[base 3]9...

and applying the log base change formula. Remember ln = log[base e]

Log[base a] b = log[base e] b / log[base e] a

So... enter the following

2*ln(9)/ln(3) = 4

However, another thing you should note is that the log is the inverse of the exponential function, and since

9^2 = 81 = 3*3*3*3 = 3^4

Remember log[base x] x = 1

Taking log base 3

Log [base 3] 3^4 = 4 log[base 3] 3 = 4 * 1 = 4

Answer 4

Use the change of base formula.

Log[base b] x = ( Log[base a] x ) / ( Log[base a] b )

If u have a TI-83, type
[ log 9² ] / [ log 3 ] =
[ log 81 ] / [ log 3 ] = 4

For this problem it would be simpler to change it to exponential form:
3^x = 9²
3^x = 3^4
x = 4

Answer 5

4

Answer 6

you don't need a calculator

log[base 3]9^2 = log[base 3]3^4
= 4log[base 3]3 since loga^b = bloga
=4 * 1 since log[base a]a = 1
=4

Answer 7

of cause u can, now the scientific calculator, like casio fx-570ES and casio fx-991Es can change the base number.
but if u wan to use other method to solve it oso can.
log[base 3]9^2
=log[base 3](3^2)^2
=log[base 3]3^4
=4 log[base 3]3 (log[base 3]3 = 1)
=4