Question

pls answer this question.

Answer 1

Well the power of 3 is 0 on the LHS as RHS has only powers of 5
Thus (2x - 8) - 2 = 0 => x=5
Also the power of 5 should be equal as terms are equal
Thus -2 = 3 - x => x= 5
Since both satisfy thus x=5
If the value from both does not come same then there is no solution but here the answer is 5

Answer 2

Solution :-

→ 3^(2x - 8)/(15)² = 125/5^x

→ 3^(2x - 8)/(3*5)² = 5³/5^x

using (a * b)^m = a^m * b^m

→ 3^(2x - 8)/(3² * 5²) = 5³ / 5^x

cross multiply,

→ 3^(2x - 8) * 5^x = 5³ * 5² * 3²

→ 3^(2x - 8) * 5^x = 3² * 5⁵

comparing ,

→ 2x - 8 = 2

→ 2x = 2 + 8

→ 2x = 10

→ x = 5

or,

→ 5^x = 5^5

→ x = 5 .

or,

→ 3^(2x - 8) * 5^x = 3² * 5⁵

→ 3^(2x - 8)/3² = 5⁵/5^x

using a^m ÷ a^n = a^(m - n) ,

→ 3^(2x - 8 - 2) = 5^(5 - x)

→ 3^(2x - 10) = 5^(5 - x)

using options now, when we put x = 5

→ 3^(2*5 - 10) = 5^(5 - 5)

→ 3^(10 - 10) = 5^0

→ 3^0 = 5^0

→ 1 = 1

therefore, value of x is equal to 5 .

Learn more :-

prove that √2-√5 is an irrational number

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