5^2x-3+5^2=26 eching

$${ 5 }^{ 2x-3 } + { 5 }^{ 2 } =26$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{2x-3}+25=26$$

Tenglamaning ikkala tarafidan 25 ni ayirish.

$$5^{2x-3}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{2x-3})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x-3\right)\log(5)=\log(1)$$

Ikki tarafini \log(5) ga bo‘ling.

$$2x-3=\frac{\log(1)}{\log(5)}$$

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

$$2x-3=\log_{5}\left(1\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$2x=-\left(-3\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{3}{2}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(5)}+\frac{3}{2}$$

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