need some assistance or guidance on a logarithmic problem.

[sportsaholic2397]

so i am suppose to solve the following problem...

LOG[sub:2hqo4jgm]4[/sub:2hqo4jgm](64)

and if i am correct log[sub:2hqo4jgm]b[/sub:2hqo4jgm] MN = log[sub:2hqo4jgm]b[/sub:2hqo4jgm] M + log[sub:2hqo4jgm]b[/sub:2hqo4jgm] N... but is that my final answer? and for this particular problem

wouldn't that be log[sub:2hqo4jgm]4[/sub:2hqo4jgm] 8 + log[sub:2hqo4jgm]4[/sub:2hqo4jgm] 8.... let me know if i am right or wrong and if wrong please show me the correct way. thanks

 

[Loren]

The definition of a log is ...

log[sub:2xx4u7r5]b[/sub:2xx4u7r5]N = x exactly when b[sup:2xx4u7r5]x[/sup:2xx4u7r5] = N.

Set your expression equal to some unknown, then convert to exponential form and solve for the unknown.

 

[Mrspi]

so i am suppose to solve the following problem...

LOG[sub:27d6trl0]4[/sub:27d6trl0](64)

and if i am correct log[sub:27d6trl0]b[/sub:27d6trl0] MN = log[sub:27d6trl0]b[/sub:27d6trl0] M + log[sub:27d6trl0]b[/sub:27d6trl0] N... but is that my final answer? and for this particular problem

wouldn't that be log[sub:27d6trl0]4[/sub:27d6trl0] 8 + log[sub:27d6trl0]4[/sub:27d6trl0] 8.... let me know if i am right or wrong and if wrong please show me the correct way. thanks

I'll do a similar problem for you.

Find log[sub:27d6trl0]2[/sub:27d6trl0] 32

Let x = log[sub:27d6trl0]2[/sub:27d6trl0] 32

As Loren pointed out, log[sub:27d6trl0]b[/sub:27d6trl0] N = x if and only if b[sup:27d6trl0]x[/sup:27d6trl0] = N

So, log[sub:27d6trl0]2[/sub:27d6trl0] 32 = x if and only if 2[sup:27d6trl0]x[/sup:27d6trl0] = 32

Now, can you write 32 as 2 raised to some power? Yes....32 is the same thing as 2[sup:27d6trl0]5[/sup:27d6trl0], so we have

2[sup:27d6trl0]x[/sup:27d6trl0] = 2[sup:27d6trl0]5[/sup:27d6trl0]

Since the bases are the same, and the expressions are equal, the exponents must be equal as well, and x = 5.

Try the same approach on your problem.