9^23/9^11=9^x eching

$$\frac { 9 ^ { 23 } } { 9 ^ { 11 } } = 9 ^ { x }$$

x uchun yechish

$$x=12$$

Logaritm ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 23 dan 11 ni ayirib, 12 ni oling.

$$9^{12}=9^{x}$$

12 daraja ko‘rsatkichini 9 ga hisoblang va 282429536481 ni qiymatni oling.

$$282429536481=9^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9^{x}=282429536481$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{x})=\log(282429536481)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(9)=\log(282429536481)$$

Ikki tarafini \log(9) ga bo‘ling.

$$x=\frac{\log(282429536481)}{\log(9)}$$

Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{9}\left(282429536481\right)$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+12$$

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