Solve x = log3 15
huh? there's nothing to solve. Just evaluate log3 15.
Now, you probably don't have a log-base-3 key on your calculator, so you have to use what you do have: ln
x = ln15/ln3
How does that work? By definition,
3^log3 15 = 15
ln(3^log3 15) = ln15
now, ln(3^p) = p*ln3, so we have
log3 15 * ln3 = ln15
log3 15 = ln15/ln3
To solve the equation x = log3 15, we need to find the value of x that satisfies the equation.
First, let's briefly review the properties of logarithms. In this case, we have a logarithm with a base of 3:
log3 15 = x
This notation means that 3 raised to the power of x equals 15. In other words, we are looking for the exponent x that will give us 15 when 3 is raised to that exponent.
To isolate the variable x, we can rewrite the equation in exponential form:
3^x = 15
Now, we can proceed to solve for x. Taking the logarithm base 3 of both sides of the equation will allow us to simplify:
log3(3^x) = log3 15
Applying the logarithmic property that states logb (b^x) = x, where b is the base, we can simplify the equation further:
x = log3 15
Now, we need to evaluate log3 15. The logarithm base 3 of 15 can be determined as follows:
To convert the equation into an exponential form, we have:
3^x = 15
Since we don't know the exact value of x, we can use a calculator to find an approximate value.
Using a scientific calculator or a calculator with a logarithmic function, we can find log3 15, which is approximately 2.732.
Therefore, the solution to the equation x = log3 15 is approximately x = 2.732.