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 $log(5.1)$ :

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

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