log_5[log_4(log_3(x))] = 1
log_5 = log with the base of 5
log_4 = log with the base of 4
log_3 = log with the base of 3
Answer: 3^1024
Too many logs in one equation. . .I don't know how to solve it
5^log_5[log_4(log_3(x))] = [log_4(log_3(x))] =5^1
4^log_4(log_3(x))= (log_3(x))=4^5 = 1024
3^log_3(x) =x =3^1024
Don't worry, I'll explain the step-by-step process to solve the given equation.
Step 1: Start by rewriting the given equation:
log_5[log_4(log_3(x))] = 1
Step 2: Apply the property of logarithms that allows you to bring the exponent down as a coefficient. In this case, the base of the first logarithm is 5, so we can rewrite the equation as:
log_4(log_3(x)) = 5^1
Step 3: Apply the same property to the second logarithm:
log_3(x) = 4^5
Step 4: Now, solve for x by eliminating the logarithm. Raise both sides of the equation to the power of the base, which is 3:
3^(log_3(x)) = 3^(4^5)
Step 5: Since the base and the exponent are the same on the left side of the equation, they cancel out, leaving us with:
x = 3^(4^5)
Step 6: Calculate the value of 4^5 using exponentiation:
4^5 = 1024
Step 7: Substitute the value of 4^5 back into the equation:
x = 3^1024
Therefore, the solution to the equation log_5[log_4(log_3(x))] = 1 is x = 3^1024.