Question

17 points!!!
What is the missing exponent?



(2^-5) ????? = 2^-15

Answer 1

`{ \left( { 2 }^( -5 ) \right) }^( x )={ 2 }^( -15 )\\ \\ { 2 }^( -5x )={ 2 }^( -15 )\\ \\ \therefore \quad -5x=-15\\ \\ \therefore \quad x=3`

Remember that:


`{ \left( { a }^( m ) \right) }^( n )={ a }^( m\cdot n )`

Answer 2

`(2^-^5) ^x = 2 ^ - ^1^5 \\ \\ ( (1)/(32) ) ^x = (1)/(32768) \\ \\ \hbox{Solve the exponent.} \\ \\ ( (1)/(32))^x = (1)/(32768) \\ \\\hbox{Take log of both sides} \\ \\ \hbox{log}} ( (1)/(32)) ^ x = log ( (1)/(32768)) \\ \\ x * log ((1)/(32) ) = log ( (1)/(32768) ) \\ \\ \bold{ (log( (1)/(32768)))/(log (1)/(32) ) } \\ \\ x = 3`

Therefore the missing exponent is 3. Which makes the equation true.