Number of solutions of log 24-3 x -6-log 29 x -6-1- is-A- 1B- 2- 0D- 3

The correct option is A 1log_2 ( 4.3^x 6/9^x 6)=1 ( 4.3^x 6/9^x 6)=2 Let 3^x = t ⇒4t 6 = 2t^2 12 ⇒ 2t^2 4t 6 =0 ⇒ t^2 2t 3 = 0 ⇒(t 3)(t+1) = 0 ⇒ 3^x = ...

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Standard XII

Mathematics

Chain Rule of Differentiation

Number of sol...

Question

Number of solution(s) of ${log}_{2} ({4.3}^{x} - 6) - {log}_{2} (9^{x} - 6) = 1,$ is-

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Solution

The correct option is A $1$
${log}_{2} (\frac{{4.3}^{x} - 6}{9^{x} - 6}) = 1$
$(\frac{{4.3}^{x} - 6}{9^{x} - 6}) = 2$
Let $3^{x} = t$
$\Rightarrow 4 t - 6 = 2 t^{2} - 12$
$\Rightarrow 2 t^{2} - 4 t - 6 = 0$
$\Rightarrow t^{2} - 2 t - 3 = 0$
$\Rightarrow (t - 3) (t + 1) = 0$
$\Rightarrow 3^{x} = 3 or 3^{x} = - 1$
$\Rightarrow 3^{x} = 3$ $or 3^{x} = - 1 (has no solution)$
$Hence, x = 1$

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Number of solution(s) of log2(4.3x−6)−log2(9x−6)=1, is-

The correct option is A 1log2(4.3x−69x−6)=1 (4.3x−69x−6)=2 Let 3x=t ⇒4t−6=2t2−12 ⇒2t2−4t−6=0 ⇒t2−2t−3=0 ⇒(t−3)(t+1)=0 ⇒3x=3 or 3x=−1 ⇒3x=3 or 3x=−1 (has no solution) Hence, x=1

Number of solution(s) of ${log}_{2} ({4.3}^{x} - 6) - {log}_{2} (9^{x} - 6) = 1,$ is-