Solve log8(log3 a) + log8(log3 a) + log8(log3 a) = 1

Question

ScanSolve AI Tutor · Accepted Answer

Huu hapa ni utatuzi wa swali lako:

Swali ni:

\log_8(\log_3 a) + \log_8(\log_3 a) + \log_8(\log_3 a) = 1

Unganisha maneno yanayofanana ya logariti.
Kuna maneno matatu yanayofanana, hivyo tunaweza kuyaunganisha kwa kuzidisha.
$3 \log_8(\log_3 a) = 1$
Gawanya pande zote mbili kwa 3 ili kutenga logariti.
$\log_8(\log_3 a) = \frac{1}{3}$
Badilisha fomu ya logariti kuwa fomu ya eksponenti.
Tunajua kwamba ikiwa $\log_b x = y$ , basi $b^y = x$ . Hapa, $b=8$ , $y=\frac{1}{3}$ , na $x=\log_3 a$ .
$\log_3 a = 8^{\frac{1}{3}}$
Rahisisha upande wa kulia.
$8^{\frac{1}{3}}$ ni sawa na mzizi wa tatu wa 8.
$\log_3 a = \sqrt[3]{8}$ $\log_3 a = 2$
Badilisha fomu hii mpya ya logariti kuwa fomu ya eksponenti.
Hapa, $b=3$ , $y=2$ , na $x=a$ .
$a = 3^2$
Kokotoa thamani ya $a$ .
$a = 9$
Jibu la mwisho ni:
$\boxed{a = 9}$

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