Explain the error in the solution below. what additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x = log533 x = 27

From step 4 to 9 is the required steps shown below.

Step-by-step explanation:

Given : Solution below,

To find : The error in the solution and what additional step needs to be completed?

Solution : The mistake is the step 3 and additional step need to be added after it.

Step 1 -

Step 2 -

Step 3 -

Step 4 -

Applying change base rule of logarithmic,

Step 5 -

Step 6 -

Step 7 -

Step 8 -

Step 9 -

From step 4 to 9 is the required steps.

We need to add two steps to the solution

We start with the equation:

log(x) - log₅(3) = 2*log₅(3).

Where we assume:

log(x) = log₁₀(x) = ln(x)/log(10)

log₅(3) = ln(3)/ln(5)

Now let's follow the steps:

step 1)

log(x)  = 3*log₅(3).

Here we just moved the constant term from the left side to the right side, this is correct.

step 2)

log(x)  = log₅(3^3).

This is correct, the coefficient can be moved to the exponent of the argument.

step 3)

x = 27

This is wrong, here you say that the arguments must be equal, but the logarithms are different logarithms. so this is incorrect.

Here we should add step 2.5)

ln(x) = ln(10)*ln(3^3)/ln(5)

Now we have:

ln(x) = ln(10)*log(27)/log(5) = 4.72

Now another step, let's say  step 2.75)

We apply the exponential equation to both sides:

Exp(ln(x)) = Exp(4.72)

x = 112.17

So we need to add two steps to the solution before step 3.

If you want to learn more about logarithmic equations, you can read:

link

answer: b)

step-by-step explanation:

its a dot plot because since the score is not high numbers.

- r3ktforgood ☕

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743