Find x, if:

(i) $l o g_{3} x = 0$

(ii) $l o g_{x} 2 = - 1$

(iii) $l o g_{9} 243 = x$

(iv) $l o g_{5} (x - 7) = 1$

(v) $l o g_{4} 32 = x - 7$

(vi) $l o g_{7} (2 x^{2} - 1) = 2$

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Solution

(i)

(ii)

(iii)

(iv)

(v)

(vi) $l o g_{7} (2 x^{2} - 1) = 2$
$7^{2}$ = $2 x^{2} - 1$
49 + 1 = $2 x^{2}$
25 = $x^{2}$
x =+ 5 or -5

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Similar questions

Find the value of the polynomial $5 x - 4 x^{2} + 3$ at
(i) $x = 0$
(ii) $x = - 1$
(iii) $x = 2$

5 x - 4 x^{2} + 3

{log}_{5} (x - 3) + \frac{1}{2} {log}_{5} 3 < \frac{1}{2} {log}_{5} (2 x^{2} - 6 x + 7)

{log}_{3} x + {log}_{\sqrt{3}} x + {log}_{\frac{1}{3}} x < 6.

5 x - 4 x^{2} + 3

{log}_{5} x + {log}_{x} \frac{x}{3} < \frac{{log}_{5} x (2 - {log}_{3} x)}{{log}_{3} x}

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