Question

X= log base 3 1/27

Answer 1

27 = x ^ -3
3 ^ 3 = 1 / (x^3) {factorise 27 and invert x^-3}
ln(3 ^3) = ln( 1 / (x^3) ) { ln both sides}
ln(3^3) = ln(1) - ln(x^3) {apply the log rule for division}
3ln(3) = 0 - 3ln(x) {ln(1) = 0 in all bases}
ln(3) = -ln(x)
-ln(3) = ln(x) {multiple both sides by -1}
ln(3 ^ -1) = ln(x) {bring the minus one back inside the log term}
3 ^ -1 = x {raising 3 to the power of -1 is 1/3}
1/3 = x

log(base x) 27 = -3
x^-3 = 27
x^-3 = 3^3
1/x^3 = 3^3
1 = (3^3)(x^3)
x^3 = 1/3^3
x^3 = 1/27
x = 1/3 answer
either one

Answer 2

That's a lot of work

since 3^3 = 27,
3^-3 = 1/27
so, log_3(1/27) is thus -3