Solve for x given that 1/2 log, 9 + log, (5x−4) = 7. The figure below represents part of a school badge. The…

Question

Solve for x given that 1/2 log, 9 + log, (5x−4) = 7. The figure below represents part of a school badge. The badge has rotation symmetry of order 4 and 0. Complete the figure to show the badge.

ScanSolve AI Tutor · Accepted Answer

Hapa kuna hatua za kutatua maswali uliyotoa: Swali la 1: Tatua kwa x kutokana na 1/2 log₂ 9 + log₂ (5x−4) = 7. Hatua ya 1: Rahisisha neno la kwanza kwa kutumia sheria ya logariti log_b (M^k) = k log_b M. 1/2 log₂ 9 = log₂ (9^(1/2)) = log₂ √(9) = log₂ 3 Hatua ya 2: Badilisha neno lililorahisishwa kwenye mlinganyo wa asili. log₂ 3 + log₂ (5x−4) = 7; Hatua ya 3: Tumia sheria ya logariti log_b M + log_b N = log_b (MN) kuunganisha maneno ya logariti. log₂ (3(5x−4)) = 7; log₂ (15x−12) = 7; Hatua ya 4: Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo. Ikiwa log_b M = N, basi b^N = M. 15x−12 = 2⁷ Hatua ya 5: Kokotoa thamani ya 2⁷. 15x−12 = 128 Hatua ya 6: Tatua mlinganyo wa mstari kwa x. 15x = 128 + 12; 15x = 140; x = 140/15 Hatua ya 7: Rahisisha sehemu. x = 28/3 Unaweza pia kuandika jibu kama nambari mchanganyiko. x = 9 1/3 Jibu la mwisho ni: x = 28/3 au 9 1/3 Swali la 2: Kamilisha umbo kuonyesha beji. Umbo lina ulinganifu wa mzunguko wa mpangilio wa 4 kuhusu kituo O. Hii inamaanisha kuwa beji nzima itaonekana sawa baada ya kuzungushwa kwa 90°, 180°, na 270° kuzunguka O. Sehemu uliyopewa ni moja ya sehemu nne zinazofanana zinazounda beji. Ili kukamilisha umbo: Chora nakala tatu zaidi za pembetatu uliyopewa. Kila nakala inapaswa kupatikana kwa kuzungusha pembetatu ya asili kwa 90°, 180°, na 270° mtawalia, kuzunguka kituo O. Pembetatu zote nne zitakutana kwenye kituo O. Kila pembetatu itakuwa na pande zenye urefu wa 3 cm na 4 cm zinazotoka O, na upande wa 2 cm unaounganisha ncha za pande hizo mbili.

Solve for x given that 1/2 log, 9 + log, (5x−4) = 7. The figure below represents part of a school badge. The badge has rotation symmetry of order 4 and 0. Complete the figure to show the badge.

Answer

Step-by-step solution

Part 1· 7 steps

Rahisisha neno la kwanza kwa kutumia sheria ya logariti $\log_b (M^k) = k \log_b M$ .

Badilisha neno lililorahisishwa kwenye mlinganyo wa asili.

Tumia sheria ya logariti $\log_b M + \log_b N = \log_b (MN)$ kuunganisha maneno ya logariti.

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa thamani ya $2^7$ .

Tatua mlinganyo wa mstari kwa $x$ .

Rahisisha sehemu.

Part 2

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Solve for x given that 1/2 log, 9 + log, (5x−4) = 7. The figure below represents part of a school badge. The badge has rotation symmetry of order 4 and 0. Complete the figure to show the badge.

Answer

Step-by-step solution

Part 1· 7 steps

Rahisisha neno la kwanza kwa kutumia sheria ya logariti log⁡b(Mk)=klog⁡bM\log_b (M^k) = k \log_b Mlogb​(Mk)=klogb​M.

Badilisha neno lililorahisishwa kwenye mlinganyo wa asili.

Tumia sheria ya logariti log⁡bM+log⁡bN=log⁡b(MN)\log_b M + \log_b N = \log_b (MN)logb​M+logb​N=logb​(MN) kuunganisha maneno ya logariti.

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa thamani ya 272^727.

Tatua mlinganyo wa mstari kwa xxx.

Rahisisha sehemu.

Part 2

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More Mathematics Questions

Rahisisha neno la kwanza kwa kutumia sheria ya logariti $\log_b (M^k) = k \log_b M$ .

Tumia sheria ya logariti $\log_b M + \log_b N = \log_b (MN)$ kuunganisha maneno ya logariti.

Kokotoa thamani ya $2^7$ .

Tatua mlinganyo wa mstari kwa $x$ .