1-log5=1/3(log1/2+log x+1/3log5
To solve the equation 1 - log5 = 1/3(log(1/2) + log(x) + 1/3log5), we can simplify it step by step using the properties of logarithms.
Step 1: Simplify the equation using the properties of logarithms.
1 - log5 = 1/3(log(1/2) + log(x) + 1/3log5)
First, let's simplify the right side of the equation by applying the properties of logarithms. According to the properties, when adding logarithms with the same base, you can multiply their arguments:
log(1/2) + log(x) + 1/3log5 = log((1/2)(x)) + log5^(1/3)
Step 2: Simplify the equation further.
1 - log5 = 1/3(log((1/2)(x)) + log5^(1/3))
From this point, let's simplify the equation by multiplying both sides by 3 to eliminate the fraction:
3(1 - log5) = log((1/2)(x)) + log5^(1/3)
Step 3: Apply logarithm properties to simplify the equation.
3 - 3log5 = log((1/2)(x)) + log5^(1/3)
Now, let's combine the logarithms on the right side of the equation using the addition property of logarithms:
3 - 3log5 = log(((1/2)(x))(5^(1/3)))
Step 4: Continue simplifying the equation.
3 - 3log5 = log(((1/2)(x))(5^(1/3)))
Now, let's solve for x by isolating it on one side of the equation.
Subtract 3 from both sides:
-3log5 = log(((1/2)(x))(5^(1/3))) - 3
Step 5: Simplify further.
-3log5 = log(((1/2)(x))(5^(1/3))) - 3
To simplify the right side, we can combine the logarithms using the division property of logarithms:
-3log5 = log(((1/2)(x))/(5^3))
Step 6: Final step to solve for x.
To isolate x, divide both sides by -3log5:
x = (5^3)/((1/2) * 10^-3)
Now, you can calculate the value of x by evaluating the right side of the equation.
1. Please state what is required: (solve for x, simplify, prove identity, etc.)
2. the parentheses are not balanced, so the expression on the right is ambiguous.
It is recommended to insert extra parentheses whenever there are fractions, divisions or square-roots.
3. in general log means logarithm to the base 10, and ln means natural logarithm, or logarithm to the base e. However, depending on the context, log can also mean either one. When posting, it is a good idea to specify the base when "log" is used, since readers do not know which log you are working on.