Question

5^x+5^(x+2)=3250 please help​

Answer 1

Solution:

Given Equation:

$\rm \longrightarrow {5}^{x} + {5}^{x + 2} = 3250$

Can be written as:

$\rm \longrightarrow {5}^{x} + {5}^{x} \cdot {5}^{2} = 3250$

$\rm \longrightarrow {5}^{x} + 25 \cdot{5}^{x}= 3250$

Let us assume that:

$\rm \longrightarrow u = {5}^{x}$

Therefore, our equation becomes:

$\rm \longrightarrow u + 25u= 3250$

$\rm \longrightarrow 26u= 3250$

$\rm \longrightarrow u= \dfrac{3250}{26}$

$\rm \longrightarrow u=125$

Substituting back the value of u in the given equation, we get:

$\rm \longrightarrow {5}^{x} =125$

$\rm \longrightarrow {5}^{x} = {5}^{3}$

Comparing base, we get:

$\rm \longrightarrow x = 3$

★ Therefore, the value of x is 3.

Answer:

• The value of x is 3.

Learn More:

Laws of exponents.

If a, b are positive real numbers and m, n are rational numbers, then the following results hold.

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$