Find the value of x 32(x+1) = 4(2-x)

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Haya Omar, tuendelee na maswali haya. Swali la 4: Step 1: Andika namba zote kwa msingi mmoja. Tunajua kuwa 32 = 2⁵ na 4 = 2². Badilisha hizi kwenye mlinganyo: (2⁵)^((x+1)) = (2²)^((2−x)); Step 2: Tumia sheria ya vipeo (a^m)ⁿ = a^(mn). 2^(5(x+1)) = 2^(2(2−x)); 2^(5x+5) = 2^(4−2x) Step 3: Linganisha vipeo kwa sababu misingi ni sawa. 5x+5 = 4−2x Step 4: Tatua kwa x. Kusanya x upande mmoja na namba upande mwingine: 5x + 2x = 4 − 5; 7x = −1; x = −1/7; x = −1/7 Swali la 5: Step 1: Weka usemi kama Y na chukua logariti pande zote mbili. Y = √3/(14.34); log Y = log ( ((1.794 × 0.0608)/(14.34))^(1/3) ); log Y = 1/3 ( log(1.794) + log(0.0608) − log(14.34) ) Step 2: Tafuta logariti za namba kwa kutumia jedwali la logariti. log(1.794) = 0.2538; log(0.0608) = 2.7839 (au −2 + 0.7839); log(14.34) = 1.1565 Step 3: Badilisha thamani za logariti kwenye mlinganyo na ufanye hesabu. log Y = 1/3 (0.2538 + 2.7839 − 1.1565); log Y = 1/3 (0.2538 − 2 + 0.7839 − 1.1565); log Y = 1/3 (−2.1188); log Y = −0.706266... Step 4: Andika upya log Y kwa mantisa chanya na utafute antilogariti. log Y = −1 + (1 − 0.706266...) = 1.2937 Tafuta antilog ya 1.2937: Y = antilog(1.2937); Y = 10⁻¹ × 10^(0.2937) Y ≈ 0.1 × 1.966 Y ≈ 0.1966 0.1966 Swali la 6: Step 1: Tafuta kigawo cha kawaida (common denominator) cha sehemu hizo. Kigawo cha kawaida ni (x−y)(x+y). (3)/(x−y) − (1)/(x+y) = (3(x+y))/((x−y)(x+y)) − (1(x−y))/((x−y)(x+y)) Step 2: Unganisha namba za juu (numerators) juu ya kigawo kimoja. (3(x+y) − 1(x−y))/((x−y)(x+y)) Step 3: Panua na kurahisisha namba ya juu. (3x + 3y − x + y)/((x−y)(x+y)) (2x + 4y)/((x−y)(x+y)) Step 4: Unaweza pia kurahisisha kigawo kwa kutumia tofauti ya miraba (a² − b² = (a−b)(a+b)). (2x + 4y)/(x² − y²) (2x + 4y)/(x² − y²)

Find the value of x 32(x+1) = 4(2−x)

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Part 4· 4 steps

Andika namba zote kwa msingi mmoja.

Tumia sheria ya vipeo $(a^m)^n = a^{mn}$ .

Linganisha vipeo kwa sababu misingi ni sawa.

Tatua kwa $x$ .

Part 5· 4 steps0.1966

Weka usemi kama $Y$ na chukua logariti pande zote mbili.

Tafuta logariti za namba kwa kutumia jedwali la logariti.

Badilisha thamani za logariti kwenye mlinganyo na ufanye hesabu.

Andika upya $\log Y$ kwa mantisa chanya na utafute antilogariti.

Part 6· 4 steps
$\frac{2x + 4y}{x^2 - y^2}$

Tafuta kigawo cha kawaida (common denominator) cha sehemu hizo.

Unganisha namba za juu (numerators) juu ya kigawo kimoja.

Panua na kurahisisha namba ya juu.

Unaweza pia kurahisisha kigawo kwa kutumia tofauti ya miraba ( $a^2 - b^2 = (a-b)(a+b)$ ).

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