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Aleksandr-060686 [28]
3 years ago
11

Can somebody explain to me how they got 3^4(x) = 3^3(x+2)? Then explain what happened to the 3 in 3^4 and the 3 in 3^3? Please a

nd thank you, I don't understand it at all.

Mathematics
1 answer:
musickatia [10]3 years ago
3 0

Answer:

x=6

Step-by-step explanation:

81^x = 27 ^(x+2)

81 = 3^4    and 27 =3^3  so replace 81 and 27 in the equation

3^4^x = 3^3^(x+2)

When we have a power to a power we can multiply the exponents

a ^b^c = a^(b*c)

3^(4x) = 3^(3*(x+2))

Since the bases are the same, the exponents  have to be the same

a^b = a^c   means b=c

4x = 3(x+2)

Now we can solve for x

Distribute

4x = 3x+6

Subtract 3x from each side

4x-3x = 3x-3x+6

x = 6

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\text {Mass of Venus =} 4.87 \times 10^{24} \text { kg}

\text {Difference = }5.97 \times 10^{24}  - 4.87 \times 10^{24}

\text {Difference = }(5.97 - 4.87) \times 10^{24}

\text {Difference = }1.1 \times 10^{24} \text { kg}


--------------- In Pure Text Format --------------
Mass of the earth = 5.97 x 10^{24} 
Mass of Venus = 4.87 x 10^{24}
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