Question

Someone pls help me.

Answer 1

Solution:

Given,

$\tt \mapsto {3}^{x + 1} + {3}^{x - 1} = 90$

• We have to find out x.

$\tt \mapsto {3}^{x} \times {3}^{1} + {3}^{x} \times {3}^{ -1} = 90$

$\tt \mapsto {3}^{x} \times ( {3}^{1} + {3}^{ -1} ) = 90$

$\tt \mapsto {3}^{x} \times \bigg( {3} + \dfrac{1}{3} \bigg) = 90$

$\tt \mapsto {3}^{x} \times \dfrac{10}{3} = 90$

$\tt \mapsto {3}^{x} = 90 \times \dfrac{3}{10}$

$\tt \mapsto {3}^{x} =27$

$\tt \mapsto {3}^{x} = {3}^{3}$

Comparing base, we get,

$\tt \mapsto x = {3}$

∆ So, the value of x is 3.

Answer:

• x = 3

Verification:

Put x = 3 in the left hand side. We get,

$\tt = {3}^{4} + {3}^{2}$

$\tt =81 + 9$

$\tt =90$

= RHS (Hence Verified)

Answer 2

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

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

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

First , We know ,

$\sf if \:{a}^{m}\:=\:{a}^{n}$

, So , m = n . because if base is same so, power will be equal .

Now,

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

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

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

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

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

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

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

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

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

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

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

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