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Question #85638

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A. S. Adikesavan

Apr 29, 2016

$x = - \frac{log 3 - log 2}{log 3} = - 0.3691$ $x =-(log 3 - log 2 )/log 3=-0.3691$ , nearly.

Explanation:

Use ${(a b)}^{n} = a^{n} b^{n}, a^{m + n} = a^{m} a^{n} and log (a^{n}) = n log a$ $(ab)^n=a^nb^n, a^(m+n)=a^ma^n and log(a^n)=n log a$

${((3) (2))}^{x + 1} = 3^{x + 1} 2^{x + 1} = 2^{x + 2}$ $((3)(2))^(x+1)=3^(x+1)2^(x+1)=2^(x+2)$ .

So, $3^{x + 1} = 2$ $3^(x+1)=2$ .

Equating logarithms and simplifying,

$x = - \frac{log 3 - log 2}{log 3} = - 0.3691$ $x =-(log 3 - log 2 )/log 3=-0.3691$ , nearly.

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