You can put this solution on YOUR website! Given:
(1)
Take the ln of each side, obeying the rule for ln of a power, ln(a^b) = b*ln(a), to get
(2) or
(3) x = ln(0.125)/ln(2)
Use your scientific calculator to get
(4) x = -3
Check your answer with (1).
Is (2^(-3) = 0.125)?
Is (0.125 = 0.125)? Yes
Answer: x = -3
You may also recognize that 0.125 = 1/8 or 1/(2^3) or 2^(-3), so you have
(5) 2^x = 2^(-3) from which you see that
(6) x = -3
If you don't see it, take the ln of each side of (5) to get
(7) x*ln(2) = (-3)*ln(2) or
(8) x = (-3)*ln(2)/ln(2) or
(9) x = -3
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