If 1- log 813x-48- log 93x-8-3- are in A-P- then the value of x equalsA- 9B- 6C- 2D- 4

The correct option is C 2Given 1, log_9 2(3^x+48), log_9(3^x 8/3), ϵ A.P. ⇒ log_9 9,1/2log_9 (3^x+48), log_9(3^x 8/3), ϵ A.P. ⇒ 9,(3^x+48)^1/2,3^x 8/3 ϵ G.P. ...

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Byju's Answer

Standard XII

Mathematics

Continuity of a Function

If 1, log 813...

Question

If 1, $l o g_{81} (3^{x} + 48), l o g_{9} ((3^{x} - \frac{8}{3})$ are in A.P., then the value of x equals

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Solution

The correct option is C 2
Given 1, $l o g_{9} 2 (3^{x} + 48), l o g_{9} (3^{x} - \frac{8}{3}), ϵ A . P .$
$\Rightarrow l o g_{9} 9, \frac{1}{2} l o g_{9} (3^{x} + 48), l o g_{9} (3^{x} - \frac{8}{3}), ϵ A . P .$
$\Rightarrow 9, (3^{x} + 48)^{\frac{1}{2}}, 3^{x} - \frac{8}{3} ϵ G . P .$ (By concept)
$\Rightarrow l o g a, l o g b, l o g c ϵ A . P .$
$∴ a, b, c ϵ G . P . ∴ 3^{x} + 48 = 9 (3^{x} - \frac{8}{3})$
${8.3}^{x} = 72$
$3^{x} = 9, 3^{x} = 3^{2} . x = 2.$

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If 1, log81(3x+48), log9((3x−83) are in A.P., then the value of x equals

The correct option is C 2Given 1, log9 2(3x+48), log9(3x−83), ϵA.P. ⇒log9 9,12log9 (3x+48), log9(3x−83), ϵA.P. ⇒9,(3x+48)12,3x−83 ϵ G.P. (By concept) ⇒log a,log b,log c ϵ A.P. ∴a,b,c ϵ G.P. ∴3x+48=9(3x−83) 8.3x=72 3x=9,3x=32. x=2.

If 1, $l o g_{81} (3^{x} + 48), l o g_{9} ((3^{x} - \frac{8}{3})$ are in A.P., then the value of x equals