Question

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Solve the equation. log(3x + 3) = log(x + 2) + log(2) Additional Materials eBook 8. [-70.78 Points] DETAILS HPRECALC5 5.5.040. Solve the equation. 3 log(x) = 4 log(27) X Additional Materials eBook 9.

Answer 1

see explanation

Explanation:

using the rules of logarithms

• log a + log b = log(ab)

• log a = log b ⇒ a = b

• nlogx = log
`x^(n)`

given

log(3x + 3) = log(x + 2) + log2 , then

log(3x + 3) = log 2(x + 2) , so

3x + 3 = 2(x + 2) , that is

3x + 3 = 2x + 4 ( subtract 2x from both sides )

x + 3 = 4 ( subtract 3 from both sides )

x = 1

--------------------------------

given

3 logx = 4 log27 , then

log x³ = log
`27^(4)` , that is

log x³ = log 531441 , so

x³ = 531441 ( take cube root of both sides )

`\sqrt[3]{x^3}` =
`\sqrt[3]{531441}`

x = 81