Question

if (5/8)^4n-4=(25/64)^3n+4, find the value of n. ​

Answer 1

Step-by-step explanation:

$( \frac{5}{8} ) {}^{4n - 4} = ( \frac{25}{64} ) {}^{3n + 4} \\ \\ ( \frac{5}{8} ) {}^{4n - 4} = ( \frac{5 {}^{2} }{8 {}^{2} } ) {}^{3n + 4} \\ \\ ( \frac{5}{8} ) {}^{4n - 4} = ( \frac{5}{8} ) {}^{2(3n + 4)} \\ \\ now \: \: compare \: powers \: of \: \frac{5}{8} \\ \\ 4n - 4 = 2(3n + 4) \\ \\ 4n - 6n = 4 + 8 \\ \\ - 2n = 12 \\ \\ n = \frac{ - 12}{2} \\ \\ n = - 6$

Answer 2

Answer:

Question:- Find the value of N

Solution:-

Right here,you got it

$( \frac{5}{8})^{4n - 4} = ( \frac{25}{64} )^{3n + 4}$

We can use an identity,if we do make the bases equal

that is

$( \frac{5}{8})^{4n - 4} = ( \frac{5}{8} )^{2 \times (3n + 4)} \\ ( \frac{5}{8})^{4n - 4} = ( \frac{5}{8} )^{6n + 8}$

We know that,if

${a}^{m} = {a}^{n} \\ m = n$

According to the identity

here it is

$4n - 4 = 6n + 8 \\ 4n = 6n + 8 + 4 \\ - 6n + 4n = 12 \\ - 2n = 12 \\ n = \frac{12}{ - 2} \\ n = - 6$

therefore the value of

n=-6

Hope it helps