I need help solving this logarithmic function: x = log3(4^3).
log3 (4^3) = 3 log3 (4)
the real problem is to find log base 3 of 4
Let x = log3(4)
then
3^x = 4
we can take base ten logs of both sides with our calculators
x log 10 (3) = log 10 (4)
x = log 10 (4) / log 10 (3)
x = .60206 / .47712
x = log3 (4) = 1.262
we want 3 x = 3.786
To solve the logarithmic function x = log3(4^3), we need to simplify the expression inside the logarithm and then evaluate it.
First, we can simplify 4^3. Remember that an exponent represents repeated multiplication. So, 4^3 is equal to 4 multiplied by itself three times: 4^3 = 4 * 4 * 4 = 64.
Now, let's substitute 64 back into the original equation: x = log3(64).
To evaluate this logarithmic expression, we need to ask ourselves: "What exponent do we need to raise 3 to in order to obtain 64?" In other words, we need to find the power to which we raise 3 to get 64.
To find this exponent, we rewrite the logarithmic equation in exponential form:
3^x = 64.
Now we can proceed by using trial and error to find the value of x. We want to find an exponent that, when we raise 3 to that power, equals 64.
By trying different values, we find that 3^4 = 81 and 3^3 = 27. Since 64 is between those two values, the exponent we are looking for is 4 (because 64 is closer to 81).
Therefore, the solution to the logarithmic function x = log3(4^3) is x = 4.