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belka [17]
1 year ago
10

Solve the following equation for X. Round your answer to four decimal places.

Mathematics
1 answer:
strojnjashka [21]1 year ago
4 0

ANSWER

x = 1.2226

EXPLANATION

To solve this equation we have to apply the property of the logarithm of the base,

\log _bb=1

Thus, we can apply the natural logarithm - whose base is e, to both sides of the equation,

\ln e^{4x}=\ln 133

Now we apply the property of the logarithm of a power,

\log a^b=b\log a

In our equation,

\begin{gathered} 4x\ln e^{}=\ln 133 \\ 4x^{}=\ln 133 \end{gathered}

Then divide both sides by 4 and solve,

\begin{gathered} \frac{4x^{}}{4}=\frac{\ln 133}{4} \\ x\approx1.2226 \end{gathered}

The solution to this equation is x = 1.2226, rounded to four decimal places.

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Answer: 36.9

Step-by-step explanation:

For this question you have to find out whether you are using Sin, Cos or Tan.

To work out which one you are using you can use SOH CAH TOA to help you.

SOH- The 'S' is for Sin, the 'O' and the 'H' is for Opposite over Hypotenuse.

CAH- The 'C' is for Cos and the 'A' and the 'H' is for Adjacent over Hypotenuse.

TOA- The 'T' is for Tan, the 'O' and the 'A is for Opposite over Adjacent.

As you have the Opposite (the side opposite the angle we're looking for) and the Adjacent (the side next to the angle were looking for) we would be using Tan.

So first you would have to write:

Tanθ=3/4

Then because we want Theta (θ) on it's own we would have to do the inverse to 'undo' the equation. Tan-1 is the inverse of Tan.

θ=Tan-1 3/4

To find the answer you would have to put it in your calculator.

θ=36.9

Hope this helps :)

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