Question

(125/8)×(125/8)*x=(5/2)*18

Answer 1

125/8 × (125/8)^x = (5/2)^18
(5/2)³×[(5/2)^3]^x = (5/2)^18

(a^m)^n = a^mn

(5/2)^3 × (5/2)^3x = (5/2)^18

a^m × a^n = a^m+n

=> (5/2)^3+3x = (5/2)^18
=> as bases are equal exponents are equal
=> 3+3x = 18
=> 3x = 15 => x = 15/3 = 5


hope this helps

Answer 2

Answer:

5 is the required value of x.

Step-by-step explanation:

Explanation:

Given in the question that, $(\frac{125}{8} )$× $(\frac{125}{8})^x$ = $(\frac{5}{2} )^{18}$

• As we know that, Subtract the exponents to divide exponents with the same base.

• And we also know that,  employ the same procedures for multiplying exponents with variables as we would for numbers

• For illustration, let's multiply $y^5$ × $y^3$. We only add the powers by the exponent rule for multiplication with the same base. It will therefore be $y^5$ × $y^3$ = $y^{5 +3}$ = $y^8$

Step 1:

From the question, we have, $(\frac{125}{8} )$× $(\frac{125}{8})^x$ = $(\frac{5}{2} )^{18}$

This can be written as, $(\frac{5^3}{2^3} )$ × $(\frac{5^3}{2^3} )^x$ = $(\frac{5}{2} )^{18}$

Now, as we know the exponent rule,$(a^m)^n = a^{m.n}$

⇒ $(\frac{5}{2} )^3$ × $(\frac{5}{2} )^{3x}$ = $(\frac{5}{2} )^{18}$

⇒ $(\frac{5}{3} )^{3 + 3x}$ = $(\frac{5}{2} )^{18}$

Now, on comparing both sides,

⇒ 3 + 3x = 18

⇒3x = 18 - 3 = 15

⇒ x= $\frac{15}{3}$ = 5

Final answer:

Hence, 5 is the required value of x

#SPJ2