Question

What is the solution of log2x + 727 = 3? (Little 2x and little 7 before the 27)

A. x=-2
B. x=2
C. x=3
D. x=4

Answer 1

remember

`log_(n)x=y` means
y is the power to which n must be raised to obtain x
aka
n^y=x

also
if a^n=b^n where n=n, then a=b



`log_(2x+7)27=3`
translate
(2x+7)^3=27
see if we can match the bases
(2x+7)^3=3^3
therefor
2x+7=3
minus 7
2x=-4
divide 2
x=-2

Answer 2

`D:2x+7 \ \textgreater \ 0\ and\ 2x+7\\eq1\\2x \ \textgreater \ -7\ and\ 2x\\eq-6\\x \ \textgreater \ -3.5\ and\ x\\eq-3\\\\\log_((2x+7))27=3\iff(2x+7)^3=27\\\\(2x+7)^3=3^3\iff2x+7=3\ \ \ |subtract\ 7\ from\ both\ sides\\\\2x=-4\ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=-2}\in D`