Question

find the value of x​

Answer 1

Answer

x=1

Step-by-step explanation:

${25}^{x} \times {16}^{x + 1} = 6400 \\ {5}^{2x} \times {2}^{4x + 4} = {2}^{8} \times 5^2 \\ {2}^{4x + 4} = {2}^{8} \\ {5}^{2x} = 5^2 \\ Equating \: the \: powers \: as \: there \: are \: same \: bases \\ 4x + 4 = 8 \\ = > 4x = 4 \\ = > x = 1 \\ 2x = 2 \\ > x = 1$

So, you can see that the value of x is 1

Note :-

• I broke out the factors of 6400 and then wrote the factors in power form....for example

6400= 2×2×2×2×2×2×2×2×5×5

So, i wrote it as 2^8 ×5^2

• To simplify it further I wrote 25^x as 5^2x and 16^x+1 as 2^4x+4.

Hit a like if YOU liked my answer!

~Soumok

Answer 2

$Given \: 25^{x} \times 16^{x+1} = 6400$

$\implies (5^{2})^{x} \times (4^{2})^{x+1} = (80)^{2}$

$\implies (5^{x})^{2} \times (4^{x+1})^{2} = (80)^{2}$

/* On doing square root both sides ,we get */

$\implies 5^{x} \times 4^{x+1} = 80$

$\implies 5^{x} \times 4^{x} \times 4 = 80$

$\implies (5 \times 4)^{x} = \frac{80}{4}$

$\implies 20^{x} = 20^{1}$

$\implies x = 1$

Therefore.,

$\red { Value \:of \:x } \green { = 1 }$

•••♪