Question

2^x=7; evaluate 4^(x-1)

Answer 1

`\sf (49)/(4)`

Explanation:

Exponent law:

`\sf (a^m)/(a^n) =a^(m-n)`

`\sf 4^(x-1)=(4^x)/(4^1)`

Write the expression 4ˣ with base 2.

We know that 4 = 2².

`\sf (4^x)/(4)=(2^(2x))/(4)\\\\`

`\sf= ((2^x)^2)/(4)\\\\\ = (7^2)/(4)\\\\=(49)/(4)`