Question

${3}^{x - 1} + {3}^{x - + 1} = 90 find \: x$
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Answer 1

||✪✪ QUESTION ✪✪||

if 3^(x-1) + 3^(x+1) = 90,, find x ?

|| ✰✰ ANSWER ✰✰ ||

we have ,

3^(x-1) + 3^(x+1) = 90

Solving it by using a^m * a^n = a^(m+n)

→ [ 3^x * 3^(-1) ] + [ 3^x * 3^1 ] = 90

Now , using a^(-b) = 1/a^b

→ [3^x * 1/3 ] + [3^x * 3 ] = 90

Taking 3^x common now, we get,

→ 3^x [ 1/3 + 3 ] = 90

→ 3^x [ (1+9)/3 ] = 90

→ 3^x (10/3) = 90

→ 3^x = 90*3/10

→ 3^x = 27

→ 3^x = 3³

Comparing now, we get, (As , base are same) .

→ x = 3.

Hence, value of X is 3.

Answer 2

$\large{\underline{\underline{\mathtt{\bf{\:QUESTION:-}}}}}$

• ${3}^{x - 1} + {3}^{x + 1} = 90\: find \: x$

$\large{\underline{\underline{\mathtt{\bf{\:ANSWER:-}}}}}$

First , We know ,

• if $\:{a}^{m}\:=\:{a}^{n}$ , So , m = n . because if base is same so, power will be equal .

Now,

$\leadsto\:{3}^{x - 1} + {3}^{x + 1} = 90$

$\leadsto\:{3}^{x}\times\:{3}^{-1}\:+\:{3}^{x}\times\:{3}^{1}\:=\:90$

$\leadsto\:{3}^{x}({3}^{-1}\:+\:3\:=\:90$

$\leadsto\:{3}^{x}(\frac{1}{3}\:+\:3)\:=\:90$

$\leadsto\:{3}^{x}(\frac{(1+9)}{3}\:=\:90$

$\leadsto\:{3}^{x}(\frac{10}{3}\:=\:90$

$\leadsto\:{3}^{x}\:=\:90\times\:\frac{3}{10}$

$\leadsto\:{3}^{x}\:=\:27$

$\leadsto\:{3}^{x}\:=\:{3}^{3}$

compare both side , here, base is same , so power will be equal each other ,

$\bold{\boxed{\boxed{\:(x)\:=\:3}}}$

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