SOLVE for x log 3 x = 4 log x = 2.6532 log 2 (x+1) = 5 2 log x = log 25

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15) Tatua kwa $x$

$\log_3 x = 4$

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.
$$ x = 3^4 $$
Kokotoa thamani.
$$ x = 3 \times 3 \times 3 \times 3 = 81 $$ $x = \boxed{\text{81}}$
2. $\log x = 2.6532$
Badilisha mlinganyo wa logariti (kwa base 10) kuwa mlinganyo wa kielelezo.
$$ x = 10^{2.6532} $$
Kokotoa thamani.
$$ x \approx 450.00 $$ $x \approx \boxed{\text{450.00}}$
3. $\log_2 (x+1) = 5$
Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.
$$ x+1 = 2^5 $$
Kokotoa $2^5$ .
$$ x+1 = 32 $$
Tatua kwa $x$ .
$$ x = 32 - 1 $$ $$ x = 31 $$ $x = \boxed{\text{31}}$
4. $2 \log x = \log 25$
Tumia kanuni ya logariti $n \log a = \log a^n$ .
$$ \log x^2 = \log 25 $$
Ikiwa $\log A = \log B$ , basi $A = B$ .
$$ x^2 = 25 $$
Tatua kwa $x$ .
Kumbuka kuwa $x$ lazima iwe chanya kwa sababu ya logariti. $x = \sqrt{25}$ $x = 5$ $x = \boxed{\text{5}}$

STRAND 3: ALGEBRA - EXPANSIONS, FACTORISATION AND QUADRARICS

Panua na Rahisisha: $3(2x-5) + 4(x+2)$
Panua vigawo vilivyo nje ya mabano.
$3(2x-5) = 6x - 15$ $4(x+2) = 4x + 8$
Mlinganyo unakuwa:
$6x - 15 + 4x + 8$
Unganisha vigezo vinavyofanana.
$(6x + 4x) + (-15 + 8)$ $10x - 7$
Jibu ni $\boxed{\text{10x - 7}}$

16) Tumia utambulisho wa quadratic kutathmini kikamilifu: $102^2$
Andika 102 kama jumla ya namba mbili.
$102 = 100 + 2$
Tumia utambulisho wa quadratic $(a+b)^2 = a^2 + 2ab + b^2$ .
Hapa, $a=100$ na $b=2$ .
$(100+2)^2 = 100^2 + 2(100)(2) + 2^2$
Kokotoa kila neno.
$100^2 = 10000$ $2(100)(2) = 400$ $2^2 = 4$
Jumlisha matokeo.
$10000 + 400 + 4 = 10404$
Jibu ni $\boxed{\text{10404}}$

SOLVE for x log 3 x = 4 log x = 2.6532 log 2 (x+1) = 5 2 log x = log 25

Step-by-step solution

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa thamani.

Badilisha mlinganyo wa logariti (kwa base 10) kuwa mlinganyo wa kielelezo.

Kokotoa thamani.

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa $2^5$ .

Tatua kwa $x$ .

Tumia kanuni ya logariti $n \log a = \log a^n$ .

Ikiwa $\log A = \log B$ , basi $A = B$ .

Tatua kwa $x$ .

Panua vigawo vilivyo nje ya mabano.

Unganisha vigezo vinavyofanana.

Andika 102 kama jumla ya namba mbili.

Tumia utambulisho wa quadratic $(a+b)^2 = a^2 + 2ab + b^2$ .

Kokotoa kila neno.

Jumlisha matokeo.

Still stuck on this one?

More Mathematics Questions

SOLVE for x log 3 x = 4 log x = 2.6532 log 2 (x+1) = 5 2 log x = log 25

Step-by-step solution

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa thamani.

Badilisha mlinganyo wa logariti (kwa base 10) kuwa mlinganyo wa kielelezo.

Kokotoa thamani.

Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo.

Kokotoa 252^525.

Tatua kwa xxx.

Tumia kanuni ya logariti nlog⁡a=log⁡ann \log a = \log a^nnloga=logan.

Ikiwa log⁡A=log⁡B\log A = \log BlogA=logB, basi A=BA = BA=B.

Tatua kwa xxx.

Panua vigawo vilivyo nje ya mabano.

Unganisha vigezo vinavyofanana.

Andika 102 kama jumla ya namba mbili.

Tumia utambulisho wa quadratic (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2.

Kokotoa kila neno.

Jumlisha matokeo.

Still stuck on this one?

More Mathematics Questions

Kokotoa $2^5$ .

Tatua kwa $x$ .

Tumia kanuni ya logariti $n \log a = \log a^n$ .

Ikiwa $\log A = \log B$ , basi $A = B$ .

Tatua kwa $x$ .

Tumia utambulisho wa quadratic $(a+b)^2 = a^2 + 2ab + b^2$ .