Question

5 to the power X added 5 to the power X+ 1 equals 15 find x ​

Answer 1

Answer:

9

Step-by-step explanation:

5 to the power X added 5 to the power X+ 1 equals 15 find

Answer 2

Question:-

➡ If $\sf 5^{x} + 5^{x+1} = 15$ then find the value of x.

Answer:-

➡ The value of x is 1 - log(2)

Solution:-

Given that,

$\sf {5}^{x} + {5}^{x + 1} = 15$

$\sf \implies {5}^{x} (1 + {5}^{1} ) = 15$

$\sf \implies {5}^{x} \times 6 = 15$

$\sf \implies {5}^{x}= \frac{15}{6}$

$\sf \implies {5}^{x}= \frac{5}{2}$

Now, taking log on both sides, we get,

$\sf \implies x = log_{5}( \frac{5}{2} )$

$\sf \implies x = log_{5}(5) - log(2)$

$\sf \implies x = 1 - log(2)$

Hence, the value of x is 1 - log(2)

Formulae Used:-

• $\sf {a}^{b} = n \implies log_{a}(n) = b$
• $\sf log_{n}( \frac{a}{b} ) = log_{n}(a) - log_{n}(b)$
• $\sf log_{n}{n}=1,(n>0, n \neq 1)$

Other Formulae:-

• $\sf log(a)+log(b)+..=log(ab..)$
• $\sf log_{a}(b) =\frac{log(b)}{log(a)}$
• $\sf log_{e}{x} = ln(x)$