Logarithms
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1. Simplify the expression: (625x^4y)^1/4 / (16xy^3)^3/4 . Assume that all variables represent positive numbers. Choose the correct answer from the following.
2. Assume that all variables are positive and multiply:
y^5/9(y -^5/9 + 5y^4/9)
3. Find the value of x: log x361/169 = 2
4. Evaluate the expression log 6 1.
5. Evaluate the expression log2 2^3
6. Assume that x, y and z are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x,y, and z.
log(10√[x9y11] / z10
7. Assume that x is a positive number. Use the logarithm properties to present the expression log(x + 9) - log x as the logarithm of a single quantity.
8. Fill in the blank to make a true statement. To solve 5 x = 27, we can take the logarithm of each side of the equation to get log (5 x ) = log (27). The power rule for logarithms would then provide a way of moving the variable x from its position as an __________ to the position of a coefficient.
9.Write the equation (1/5)^-6 = 15625 in logarithmic form.
10. Find the value of x: log3 27 = x
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