Question

А) 5^(x-2)=125 б) (1/6)^(x+10)=216

Answer 1

$\displaystyle \tt a). \ 5^{x-2}=125\\\\{} \ \ \ \ \ 5^{x-2}=5^{3}\\\\{} \ \ \ \ \ x-2=3\\\\{} \ \ \ \ \ x=5\\\\\\b). \ \bigg(\frac{1}{6}\bigg)^{x+10}=216\\\\{} \ \ \ \ \ 6^{-x-10}=6^{3}\\\\{} \ \ \ \ \ -x-10=3\\\\{} \ \ \ \ \ \ x=-13$

Answer 2

Ответ: а) 5^(x-2)=125⇒х-2=3⇒х=3+2=5.

б) (1/6)^(x+10)=216⇒х+10=-3⇒х=-3-10=-13.

Объяснение:

Answer 3

To solve the equations, we need to find the values of 'x' that satisfy each equation. Let's tackle them one by one:

a) $5^{(x-2)} = 125$

Step 1: Express both sides with the same base, which is 5: $125 = 5^3$ (since $5^3 = 5 \times 5 \times 5 = 125$)

Step 2: Now that both sides have the same base, we can equate the exponents: $x - 2 = 3$

Step 3: Solve for 'x': $x = 3 + 2$ $x = 5$

So, the solution for equation (a) is $x = 5$.

b) $(1/6)^{(x+10)} = 216$

Step 1: Express both sides with the same base. Since $216$ is not a power of $1/6$, let's express $216$ as a power of $6$: $216 = 6^3$ (since $6^3 = 6 \times 6 \times 6 = 216$)

Step 2: Now that both sides have the same base, we can equate the exponents: $x + 10 = 3$

Step 3: Solve for 'x': $x = 3 - 10$ $x = -7$

So, the solution for equation (b) is $x = -7$.

To summarize: a) The solution for $5^{(x-2)} = 125$ is $x = 5$. b) The solution for $(1/6)^{(x+10)} = 216$ is $x = -7$.