Mathematics: Solve each of the following equations. ㏒₇(9x+38) - ㏒₇(x+2) = ㏒₉81

find the measure of each angle pls help ...

Solve each of the following equations. ㏒₇(9x+38)

Ответ:

jessicawelch25

14.03.2022

First you need to determine the defined range
$log_{7}$ (9x + 38) - $log_{7}$ (x + 2) = $log_{9}$ (81), x∈ (-2, + ∞)using the $log_{a}$ (x) - $log_{a}$ (y) = $log_{a}$ ( $\frac{x}{y}$ ), simplify the expression
$log_{7}$ ( $\frac{9x+38}{x+2}$ ) = $log_{9}$ (81)
write the number in the second set of parenthesis in exponential form
$log_{7}$ ( $\frac{9x+38}{x+2}$ ) = $log_{9}$ (9²)
using $log_{a}$ ( $a^{x}$ ) = x, simplify the expression
$log_{7}$ ( $\frac{9x+38}{x+2}$ ) = 2
the expression $log_{a}$ (x) = b is equal to x = $a^{b}$
$\frac{9x+38}{x+2}$ = 7²
evaluate the power
$\frac{9x+38}{x+2}$ = 49
multiply both sides of the equation by x + 2
9x + 38 = 49(x + 2)
distribute 49 through the parenthesis
9x + 38 = 49x + 98
move the variable to the left side and change its sign
9x - 49x + 38 = 98
move the constant to the right side and change its sign
9x - 49x = 98 - 39
collect the like terms
-40x = 98 - 38
subtract the numbers
-40x = 60
divide both sides of the equation by -40
x = - $\frac{3}{2}$ , x ∈ (-2, + ∞)
finally,, check if the solution is in the defined range
x = - $\frac{3}{2}$
this means that the correct answer to your question is x = - $\frac{3}{2}$
let me know if you have any further questions
:)

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Solve each of the following equations. ㏒₇(9x+38) - ㏒₇(x+2) = ㏒₉81

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