Question

4. Find the value of p if 2P=2^2 p-7

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Answer 1

P = 7

Explanation:

`{ \tt{ {2}^(p) = {2}^(2p - 7) }} \\`

- From the law of indices; If an index has same base, then the powers are equal.

`{ \boxed{ \rm{ \blue{ ({x}^(a) = {x}^(b)) \rightarrow{ \red{a = b}} }}}}`

`{ \tt{p = 2p - 7}} \\ { \tt{p -2 p = - 7}} \\ { \tt{p = 7}}`

OR:

Applying logarithms can also be borrowed;

`{ \tt{ log( {2}^(p) ) = log( {2}^(2p - 7) ) }} \\ \\ { \tt{p log(2) = (2p - 7) log(2) }} \\ \\ { \tt{ (p log(2) )/( log(2) ) = ((2p - 7) log(2) )/( log(2) ) }} \\ \\ { \tt{p = 2p - 7}} \\ \\ { \tt{p - 2p = - 7}} \\ \\ { \tt{p = 7}}`