Some LOGs help please! (1 Viewer)

[0hNivlek]

So my school gave us holiday hw but i don't understand some of it. How do you solve these?

1. If a ^ (2.37) = 10, find:
a) log a 10

2. Express as a logarithm to the given base:
a) log 4 ^ 11 (base 2)

Thanks!

 

[gurmies]

1. If a ^ (2.37) = 10, find:
a) log a 10

2. Express as a logarithm to the given base:
a) log 4 ^ 11 (base 2)

1 a) log a 10 = 2.37

2 a) logbase2 (4^11)/logbase2 (10) - assuming initial base was 10

 

[alcalder]

The thing with logs is, they are reciprocals of powers.

1. So, if something to a power is 10
eg a ^2.37 = 10

Then the reciprocal is, the log (to the base of the number you are using in the power) of the answer is the power.
log _a 10 = 2.37

2. If you want to change the base from say "10" (assumed if no log base is given) to "2", you divide as shown:

log ₁₀ 4¹¹= log₂4¹¹ / log₂10

=log₂2²⁽¹¹⁾ / log₂10
=log₂2²² / log₂10
=22/log₂10

 

[Trebla]

They're not "reciprocals". They're called "inverses".

 

[0hNivlek]

Wow thanks for the help guys

 

[iiinsane02]

Phew, lucky I don't do Logs anymore in the 2u Mathematics course.

I miss Ms Diep