Question

5^(x-1)+5*0,2^(x-2)=26

Answer 1

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Answer 2

To solve the equation 5^(x-1) + 5 * 0.2^(x-2) = 26, we'll follow these steps:

Step 1: Simplify the equation. Step 2: Use algebraic techniques to solve for x.

Let's start with step 1:

5^(x-1) + 5 * 0.2^(x-2) = 26

Step 2: We can rewrite 0.2 as 1/5, as 0.2 = 1/5.

5^(x-1) + 5 * (1/5)^(x-2) = 26

Now, we can simplify the second term, (1/5)^(x-2) as follows:

(1/5)^(x-2) = 5^(2-x)

Substitute this back into the equation:

5^(x-1) + 5 * 5^(2-x) = 26

Now, both terms on the left side of the equation have the same base (5), so we can combine them into one term using the rules of exponents:

5^(x-1) + 5^(1 + 2-x) = 26

Now, we have the bases as 5^(x-1) and 5^3, which is 125:

5^(x-1) + 5^3 = 26

Rearrange the equation:

5^(x-1) = 26 - 125

5^(x-1) = -99

Now, to isolate x, we can take the logarithm of both sides. Let's use the natural logarithm (ln) here:

ln(5^(x-1)) = ln(-99)

Apply the logarithm property that ln(a^b) = b * ln(a):

(x-1) * ln(5) = ln(-99)

Finally, solve for x:

x - 1 = ln(-99) / ln(5)

x = 1 + ln(-99) / ln(5)

It appears that the result for x is a complex number because ln(-99) is not a real number. Thus, the equation might not have a real solution.

Keep in mind that solving equations involving powers might lead to complex solutions or no real solutions. You might want to double-check the original equation or provide additional context if you believe there is a mistake.