y=a^x-(b+1) eching

$$y = a ^ { x } - ( b + 1 )$$

b uchun yechish (complex solution)

$$b=-y+a^{x}-1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

b+1 teskarisini topish uchun har birining teskarisini toping.

$$y=a^{x}-b-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$a^{x}-b-1=y$$

Ikkala tarafdan a^{x} ni ayirish.

$$-b-1=y-a^{x}$$

1 ni ikki tarafga qo’shing.

$$-b=y-a^{x}+1$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-b}{-1}=\frac{y-a^{x}+1}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$b=\frac{y-a^{x}+1}{-1}$$

y-a^{x}+1 ni -1 ga bo'lish.

$$b=-y+a^{x}-1$$

b uchun yechish

$$b=-y+a^{x}-1$$

$$\left(a<0\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }\left(a=0\text{ and }x>0\right)\text{ or }a>0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

b+1 teskarisini topish uchun har birining teskarisini toping.

$$y=a^{x}-b-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$a^{x}-b-1=y$$

Ikkala tarafdan a^{x} ni ayirish.

$$-b-1=y-a^{x}$$

1 ni ikki tarafga qo’shing.

$$-b=y-a^{x}+1$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-b}{-1}=\frac{y-a^{x}+1}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$b=\frac{y-a^{x}+1}{-1}$$

y-a^{x}+1 ni -1 ga bo'lish.

$$b=-y+a^{x}-1$$

a uchun yechish (complex solution)

$$a=e^{\frac{Im(x)arg(y+b+1)+iRe(x)arg(y+b+1)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2iRe(x)\pi n_{1}}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\left(|y+b+1|\right)^{\frac{Re(x)-iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$