Question

if (3^3x-1)/9=27 find the value of x​

Answer 1

Question :

• $\sf If\: \dfrac{3^{3x-1}}{9} = 27 \:, Find\:the\:value\:of\:x.$

Solution:

$\longmapsto\dfrac{3^{3x-1}}{9} = 27$

❖ Cross multiplying:-

$\\\sf\dashrightarrow 3^{3x-1} = 27 \times 9 \\\\ \sf\dashrightarrow 3^{3x-1} = 243 \\\\\sf\dashrightarrow 3^{3x-1} = 3^5$

❖ Bases are same , Powers will be taken equal :-

$\sf\longmapsto 3^{3x-1} = 3^5 \\\\ \sf\dashrightarrow 3x-1=5 \\\\\dashrightarrow \sf 3x=5+1 \\\\\dashrightarrow \sf 3x=6 \\\\\dashrightarrow \sf x = \cancel{\dfrac{6}{3}} \\\\\sf \dashrightarrow \underline{\boxed{\pink{\mathfrak x = 2}}}$

More to know :

• $\sf a^m\times a^n = a^{m+n}$
• $\sf (a^m)^n = a^{mn}$
• $\sf a^1 = a$
• $\sf a^0 = 1$
• $\sf a^{-m}=\frac{1}{a^m}$
• $\sf a^{m/n}=\sqrt[m]{a^n} = \sqrt[m]{a}\;^n$
• $\sf a^m = a^n \: , then \: m= n$