Transforming logarithmic functions

Question

B=5·8^2t into t=1/2 · log₈ (1/5 B)

 

 

I need an explanation how to solve this step by step, so I can better understand how to tackle problems which are similar.

 

Thank you!

Answer 1

B = 5·8^2t

 

B/5 = 8^2t

 

To get the t out of the exponent, use log base 8: Log₈(8^2t) = 2t

 

log₈(B/5) = 2t

 

(1/2)log₈(B/5) = t      [Note: B/5 = 1/5 B]