Question

27^b=531441 Solve for b

Answer 1

Step 1

Given;

$27^b=531441$

Required; To find the value of b

Step 2

Find the value of b

$\begin{gathered} \text{Method 1} \\ 531441=27^4 \\ \text{Hence, } \\ 27^b=27^4 \\ \text{cancelling out the base 27 yields, b= 4} \\ OR \\ \log 27^b=\log 531441 \\ b\log 27=\log 531441 \\ b=\frac{\log 531441}{\log 27} \\ b=4 \end{gathered}$

Hence, b=4