Question

1.√3×3^2x=1/9 2.5^x-7×5^x-2=90

Answer 1

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Answer 2

To solve the equations, you'll want to isolate the variable x in each equation. Let's start with the first equation:

1. √3 * 3^2x = 1/9

To solve for x, we need to get rid of the square root. First, square both sides to eliminate the square root:

(√3 * 3^2x)^2 = (1/9)^2

3 * 3^4x = 1/81

Now, simplify the equation:

3 * 81x = 1/81

Multiply both sides by 81 to isolate x:

3 * 81x * 81 = (1/81) * 81

243x = 1

Now, divide both sides by 243 to solve for x:

x = 1/243

So, the solution to the first equation is x = 1/243.

Now, let's move on to the second equation:

2. 5^x - 7 * 5^(x-2) = 90

To solve for x, first, notice that you can rewrite the equation using a common base:

5^x - 7 * (5^x * 5^(-2)) = 90

Now, simplify further:

5^x - 7 * (5^x / 25) = 90

Next, combine the terms with 5^x:

5^x - (7/25) * 5^x = 90

Now, factor out 5^x:

5^x(1 - 7/25) = 90

Simplify the fraction:

5^x(18/25) = 90

Now, divide both sides by (18/25) to solve for x:

5^x = 90 / (18/25)

5^x = (90 * 25) / 18

5^x = 125

To find x, take the logarithm of both sides (with base 5):

x = log5(125)

x = 3

So, the solution to the second equation is x = 3.