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=(\log 531441)/(\log 27) \\ b=4 \end{gathered}`

Hence, b=4