Table of Contents
Practice Problems on logarithms
I) write the following in the logarithmic format
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$5^3$ = 125
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$2^4$ = 16
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$4^{-2}=\frac{1}{16}$
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$(\frac{1}{2})^{-3}=8$
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$\sqrt {81}$ = 9
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$x^{2a}=y$
II) convert the following logarithms into exponents
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x= $log_3\ y$
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$log_x\ 1$ =0
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ln x = 5
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$log\ 100=2$
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$log_8\ 2=\frac{1}{3}$
III) Find the values of x
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$log_5\ 25$ = x
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$log_{100}\ 1000$ = x
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$log_{23}\ 1$ = x
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$log_3\ \frac{1}{27}$ = x
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$log_x\ 49$ = 7
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$log_9\ x$ = -3
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$log_5\ \frac{1}{5}$ = x
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$log_8\ x=1- \frac{1}{2}$
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$log_{12}\ 1$ = x
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$log_{32}\ 2$ = x
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$log_4\ \frac{1}{32}$ = x
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$log_{12}\ \frac{1}{144}$ = x
IV) Write the following expressions in terms of logs of x, y and z
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log $x^3y$
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log $xyz$
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log $\sqrt[3]x y^2 z$
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log $\frac{x}{z^3}y$
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log $\sqrt[5]{x^3yz^2}$
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log $x \sqrt{ \frac{\sqrt{x^3y^2}}{z^4}}$
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log $(x^3y)^{\frac{1}{2}}$
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log $\frac{x^3}{y}$
V) Solve the following logarithmic equations
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ln x =-2
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log (7x+2) = 2
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log x + log (x+1) = log 4x
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2log x = log 2 + log(3x-4)
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$log_3\ (x+3) + log_3\ (x+2) - log_3\ 10 = log_3\ x$
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$log_2\ x + log_2\ (x+3) = 1$
VI) If log 2= x, log 3 =y then express the following in x and y
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log 24
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log 225
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log 150
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$log_7\ 980$
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log 343
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log 12.5
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log 0.2
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log 15
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log 2.5
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$log_7\ 3.5$
VII) Solve the following equations
- $3^x$ - 1 =8
- $2^{2x}-2^x-6$=0
- $3^{1-x}=5^x$
- $3^{2x-1}+3{x+2}-18$=0
- $e^{2x}-2e^{x}-15$=0
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