Question

a common mistake people make when working with exponents is to multiply the base by the exponent instead of raising the base to the power of the exponent. For instance, they would mistakenly say that 2^3 is 6 (because 2x3=6) when the correct answer is actually 8 (2x2x2=8) are there any pairs of numbers for which this mistake in thinking actually gives the correct answer? In other words are there any solutions to the equation a^x=a X what are the?

Answer 1

The pair of number are (2 and 1), (2 and 2)

Explanation:

The pair of number that makes the expression
`a^x = ax` true are 2 and 2 as shown:

where a = 2 and x =2

2² = 2*2

2² = 4

and:

2*2 = 4

Hence 2² = 2(2) = 4 making the expression
`a^x = ax` true for both pair of numbers

Also the number pair 1 and 2 makes the expression correct as shown:

`2^1 = 2(1)\\2 = 2 (true)`