Urgent Help need for a Log problem.

[0rmus]

Hi folks, I've been stumped by this question on my latest assignment which is due tomorrow. The Question : If log2 y = 15 , find the value of log2 8y Any help from you math guru's out there would be greatly appreciated. Thanks 0rmus

 

[MarkFL]

First, use the property:

\(\displaystyle \log_a(bc)=\log_a(b)+\log_a(c)\)

Then you have two terms. For the term which you are not given the value, try to write the argument as a power of 2, then apply the properties:

\(\displaystyle \log_a(b^c)=c\cdot\log_a(b)\)

\(\displaystyle \log_a(a)=1\)

Now, what do you find?

 

[JeffM]

Hi folks, I've been stumped by this question on my latest assignment which is due tomorrow. The Question : If log2 y = 15 , find the value of log2 8y Any help from you math guru's out there would be greatly appreciated. Thanks 0rmus

An alternative way to attack this is

\(\displaystyle log_2(y) = 15 \implies y = 2^{15} \implies 8y = what?\)

Can you answer the question now?

 

[soroban]

Hello, 0rmus!

\(\displaystyle \text{If }\log_2(y) = 15\text{, find the value of }\log_2(8y)\)

We have: .\(\displaystyle \log_2(8y) \;=\;\underbrace{\log_2(8)}_{\text{This is 3}} + \underbrace{\log_2(y)}_{\text{This is 15}} \;=\;3 + 15 \;=\;18 \)