Solve 2^(3x-4)=5 round to the nearest ten-thousandth

2 answers:

4 0

2^(3x-4)=5
ln(2^(3x-4)=ln 5
(3x-4)ln 2=ln 5 (log_a x^n=n*log_a x)
3x-4=ln 5/ln 2
3x=(ln 5 / ln 2)+4
x=[(ln 5 / ln 2)+4]/3
x≈2.1073

Answer: x=[(ln 5/ln 2) +4]/3 (≈2.1073)

noname [10]3 years ago

3 0

You can use logarithm for this question:
If you convert the provided equation into logarithm, you should get:
Log _2 5= (3x-4)
You plug log_2 (5) into a calculator, I dont have one with me so you will have to do the calculation, then solve for x

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a. Please find attached the required diagram created with MS Visio

b. Paul's distance travelled east is approximately 11.98 km

Paul's distance travelled south is approximately 0.903 km

<h3>Method used for diagram and for the distance calculation</h3>

Given:

The distance Paul runs = 1.5 km

The bearing Paul is running = 127°

a. The bearing of path Paul runs, 127°, is the angle measured in the clockwise direction relative to the northern direction

Please find attached the diagram representing the situation, created with MS Visio.

b. Paul's distance travelled east relative to the starting point is given by the component of Paul's path in the x-axis direction which is found as follows;