Question

Log4×log2×log3(x)≤5​

Answer 1

$log_4log_2log_3x\leq 5\; \; ,\; \; \; ODZ:\; x>0\\\\log_4(log_2log_3x)\leq log_44^5\; \; \; \Rightarrow \; \; \; log_2log_3x\leq 4^5\; ,\; \; log_2log_3x\leq 1024\; ,\\\\log_2(log_3x)\leq log_22^{1024}\; \; \; \Rightarrow \; \; \; log_3x\leq 2^{1024}\; ,\\\\log_3x\leq log_33^{2^{1024}}\; \; \; \Rightarrow \; \; \; x\leq 3^{2^{1024}}\\\\Otvet:\; \; 0$

Answer 2

To solve the inequality log4 × log2 × log3(x) ≤ 5, we need to simplify it step by step.

First, let's apply the properties of logarithms to simplify the expression:

log4 × log2 × log3(x) = (log(x) / log(4)) × (log(x) / log(2)) × (log(x) / log(3))

Next, we can combine the logarithms using the property log(a) + log(b) = log(a * b) to simplify further:

(log(x) / log(4)) × (log(x) / log(2)) × (log(x) / log(3)) = log(x)³ / (log(4) × log(2) × log(3))

Now, we can rewrite the inequality as:

log(x)³ / (log(4) × log(2) × log(3)) ≤ 5

To solve for x, we can isolate log(x)³ on one side:

log(x)³ ≤ 5 × (log(4) × log(2) × log(3))

Now, we can take the cube root of both sides to eliminate the cube:

log(x) ≤ (5 × (log(4) × log(2) × log(3)))^(1/3)

Finally, we can exponentiate both sides using the base 10 to solve for x:

x ≤ 10^[(5 × (log(4) × log(2) × log(3)))^(1/3)]

Please note that calculating the exact numerical value requires substituting the logarithmic values into the equation, which I can't provide without specific logarithmic values. However, you can use a calculator to evaluate the expression and obtain the approximate solution for x.