MIke is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

Mathematics

2 answers:

Rudiy273 years ago

7 0

Answer:

x=0.6882

In order to solve this problem, we must use logs, from either base.

We must first take the log of both sides, which will give us log 37^x=log 12. Then we have to multiply x by log(37), due to the power rule of logs, so we will now have x times log(37)=log (12). Afterwards, we have to divide both sides by log (37), so the equation will become x=log (12) / log (37) --> x=1.079/1.568, and our final simplifed answer will be 0.6882. We can then simply input the value of x into the original equation to check, and then we will know it is the correct answer.

Yanka [14]3 years ago

4 0

Answer:

Start by getting the x to be alone

Step-by-step explanation:

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Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the

Neko [114]

Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

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Start End

Second year $\frac{5}{4}x$ -------------- $\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x$

Third year $(\frac{5}{4} )^{2}x$ ------------- $(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x$

Fourth year $(\frac{5}{4})^{3}x$ -------------- $(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.$