To solve the equation log4(2) * log4(5x) = 18, we will first rewrite the logarithms and simplify the problem.
1. First, observe that log4(2) can be calculated as follows:
Since 4 = 22, we can use the change of base formula:
log4(2) = 1/2
2. Next, substitute this value back into the equation:
(1/2) * log4(5x) = 18
3. Multiply both sides of the equation by 2 to eliminate the fraction:
log4(5x) = 36
4. Now, we can rewrite the logarithmic equation in exponential form:
5x = 436
5. To isolate x, divide both sides by 5:
x = (436)/5
Hence, the potential solution to the given equation is:
x = (436) / 5
This solution shows that x can be expressed as a significant power of 4 divided by 5. This indicates how logarithmic relationships can lead to unexpected yet precise results.