SOLUTION: Please help with this. I can't understand the way my teacher is trying to explain. Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2 evaluate the following: 1. l

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help with this. I can't understand the way my teacher is trying to explain. Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2 evaluate the following: 1. l      Log On


   



Question 563705: Please help with this. I can't understand the way my teacher is trying to explain.
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:
1. log (b)15
2. log (b).6
3. log (b)125
4. log (b)(^3sqrt(3))^7
Thank you so much for your help

Found 2 solutions by Alan3354, Tatiana_Stebko:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:
1. log (b)15
15 = 3*5
Multiplying --> adding the logs
log%28b%2C15%29+=+log%28b%2C3%29+%2B+log%28b%2C5%29+=+3.7
-----------------
2. log (b).6
0.6 = 3/5
Subtract logs when dividing
= log(3) - log(5) = -0.7
----------------
3. log (b)125
125+=+5%5E3
= 5*5*5
log(125) = log(5) + log(5) + log(5)
= 3*log(5)
Multiply the log by the exponent when raising to a power.
= 6.6
----------------
4. log (b)(^3sqrt(3))^7
If you mean log%28b%2C%28root%283%2C3%29%5E7%29%29
= 7%2Alog%28b%2C%28root%283%2C3%29%29%29 Multiply by the exponent
root%283%2C3%29+=+3%5E%281%2F3%29
log%283%5E%281%2F3%29%29+=+%281%2F3%29%2Alog%283%29+=+0.5 Multiply the log by the exponent
--> 7*0.5 = 3.5

Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
1. log+%28b%2C15%29=log+%28b%2C%283%2A5%29%29=log+%28b%2C3%29%2Blog+%28b%2C5%29=1.5%2B2.2=3.7
Use the properties of logarithm log+%28b%2C%28a%2Ac%29%29=log+%28b%2Ca%29%2Blog+%28b%2Cc%29
2.+log+%28b%2C0.6%29=log+%28b%2C%283%2F5%29%29=log+%28b%2C3%29-log+%28b%2C5%29=1.5-2.2=-0.7
Use the properties of logarithm log+%28b%2C%28a%2Fc%29%29=log+%28b%2Ca%29-log+%28b%2Cc%29
3. log+%28b%2C125%29=log+%28b%2C%285%5E3%29%29=3%2Alog+%28b%2C5%29=3%2A2.2=6.6
Use the properties of logarithm log+%28b%2C%28a%5En%29%29=n%2Alog+%28b%2Ca%29
4.