How do you solve for T in #2 = (5.1)^T #?

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Answer 1 · 2016-09-04T10:09:07

#T=0.4254#

As #2=5.1^T#

#T=log_5.1 2#

= #log2/log5.1#

= #0.3010/0.7076#

= #0.4254#

Answer 2 · 2016-09-04T13:59:14

#T = (log(2)) / (log(5.1))#

We have: #2 = (5.1)^(T)#

Let's apply logarithms to both sides of the equation:

#=> log(2) = log(5.1^(T))#

Using the laws of logarithms:

#=> T log(5.1) = log(2)#

We can finally solve for #T# by dividing both sides by #log(5.1)#:

#=> T = (log(2)) / (log(5.1))#