plwase sokve ittt
write 1/81 as a power of 3
Answers
Answer:
CERTIFIED EDUCATOR
1/81 = 3^x
(I) Using algebraic method.
Express 81 with its prime factors.
1/3^4 = 3^x
Apply the negative exponent rule which which is 1/a^m=a^(-m) .
3^(-4)=3^x
Since both sides of the equation has the same base 3, equate the exponents of each side equal to each other.
-4=x
Hence, the solution is x=-4 .
(II) To bring down x, apply the power rule of logarithm which is
log_b m^a = a log_bm . So take the logarithm of both sides, with a base of 3.
log_3 1/81 = log_3 3^x
log_3 1/81 = x log_3 3
At the left side of the equation, apply the quotient rule of logarithm log_b (m/n) = log_b m - log_b n .
log_3 1 - log_3 81 = x log_3 3
Express 81 with its prime factors.
log_3 1 - log_3 3^4 = x log_3 3
log_3 1 - 4log_3 3 = x log_3 3
Note that a logarithm of 1 is always equal to zero ( log_b 1 = 0 ).Also, if the base and argument are the same, then the logarithm is equal to one (log_b b = 1 ).
0 -4(1) = x(1)
-4=x
Hence, x=-4 .
1/81
= 1/3 × 3 × 3
= 1/3³
= 3‐³