Question

If ( 3^9*3^-5)^x=27 then x=?​

Answer 1

Answer:

${( {3}^{9} \times {3}^{ - 5} ) }^{x} = 27 \\ ( {3}^{9 - 5} ) {}^{x} = 27 \\ ( {3}^{4} ) {}^{x} = {3}^{3} \\ {3}^{4x} = {3}^{3} \\ 4x = 3 \\ x = \frac{3}{4}$

Answer 2

Question:-

$if \: {( {3}^{9} \times {3}^{ - 5} )}^{x} = 27 \: \: then \: \: x =$

Useful formulae:-

${a}^{m} \times {a}^{n} = {a}^{m + n}$

${( {a}^{m} )}^{n} = {a}^{mn}$

Solution:-

First Simplify

${3}^{9} \times {3}^{ - 5} = {3}^{9 + ( - 5)}$

$= > {3}^{9 - 5}$

$= > {3}^{4}$

Then,

$({ {3}^{4}) }^{x} = 27$

27 can be written as 3³

So,

${3}^{4x} = {3}^{3}$

Bases are equal.So, powers also equal

So,

$4x = 3$

$x = \frac{3}{4}$