Respuesta :

tgordon9158

To find the value of d in the given equation, we need to solve for d by using the property of exponents that states that the exponent of a power of a number is equal to the product of the exponents of the factors. In this case, we have 5^d÷5^3 = 5^18, so we can write:

5^d / 5^3 = 5^18

Since the bases of the two powers are the same (5), we can set the exponents equal to each other and solve for d:

d / 3 = 18

d = 3 * 18

d = 54

Therefore, the value of d in the given equation is 54.

semsee45

Answer:

d = 21

Step-by-step explanation:

Given equation:

[tex]5^d \div 5^3=5^{18}[/tex]

Multiply both sides by 5³:

[tex]\implies 5^d=5^{18} \times 5^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 5^d=5^{18+3}[/tex]

[tex]\implies 5^d=5^{21}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies d=21[/tex]

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