Solved on Feb 03, 2024

Solve for xx without a calculator: lnx3=4\frac{\ln x}{3} = 4

STEP 1

Assumptions
1. The natural logarithm function is denoted as ln\ln.
2. We are solving for the variable xx.
3. The equation to solve is lnx3=4\frac{\ln x}{3} = 4.
4. We will use the properties of logarithms and exponential functions to solve for xx.

STEP 2

To isolate lnx\ln x, we need to eliminate the denominator. We can do this by multiplying both sides of the equation by 3.
3lnx3=343 \cdot \frac{\ln x}{3} = 3 \cdot 4

STEP 3

Simplify both sides of the equation.
lnx=12\ln x = 12

STEP 4

To solve for xx, we need to get rid of the natural logarithm. We can do this by using the property that if lna=b\ln a = b, then a=eba = e^b, where ee is the base of the natural logarithm.
x=e12x = e^{12}
x=e12x = e^{12} is the solution to the equation lnx3=4\frac{\ln x}{3} = 4.

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