Log base 5 of 16 cubed. Times log base 11 of 6 squared. Equals logx.
logx=log5(16^3)log11(6)^2
logx=6log5(16)log11(6)
I don't know what your question is, nor do I know the base of the logx.
(log5 16^3 )(log11 6^2 = log x
3(log16/log5)(2)(log6/log11) = logx
6(log16/log5)(log6/log11)
6(1.28724...) = logx
7.72346...
x = 10^7.72346..
x = appr 52,900,679
I was using the log properties:
log a^n = n loga , and
log a b = logb/loga
To solve this problem step-by-step, we'll use logarithmic properties:
Step 1: Rewrite the equation using the exponential form of logarithms:
5^(log base 5 of 16^3) * 11^(log base 11 of 6^2) = x
Step 2: Simplify the exponents using logarithmic properties:
5^3 * 11^2 = x
Step 3: Calculate the values on the right side of the equation:
125 * 121 = x
Step 4: Evaluate the product on the right side of the equation:
x = 15,125
Therefore, log base 5 of 16^3 times log base 11 of 6^2 equals log base x, where x is equal to 15,125.
To solve the equation:
log base 5 of 16 cubed * log base 11 of 6 squared = log base x
We can simplify each logarithmic expression separately using the properties of logarithms.
First, let's simplify log base 5 of 16 cubed:
log base 5 of 16 cubed
Using the exponent property of logarithms, which states that log base a of b^c is equal to c times log base a of b, we can rewrite the expression as:
3 * log base 5 of 16
Now, let's simplify log base 11 of 6 squared:
log base 11 of 6 squared
Again, using the exponent property of logarithms, we can rewrite the expression as:
2 * log base 11 of 6
Now, let's substitute these simplified expressions back into the original equation:
3 * log base 5 of 16 * 2 * log base 11 of 6 = log base x
Combining the two logarithmic expressions:
6 * log base 5 of 16 * log base 11 of 6 = log base x
To find the value of log base x, we need to know the exact values of log base 5 of 16 and log base 11 of 6. To compute these values, we can use a calculator or a mathematical software.
Let's assume that the logarithmic values are approximately:
log base 5 of 16 ≈ 2.3219
log base 11 of 6 ≈ 0.6990
Now we can substitute these values into the equation:
6 * 2.3219 * 0.6990 = log base x
14.5234 ≈ log base x
To find the value of x, we need to convert the logarithmic equation into exponent form. In exponent form, the base is raised to the power equal to the logarithmic value. In this case:
x ≈ 10^14.5234
Using a calculator, the approximate value of x is:
x ≈ 28774597.77