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

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: