Name Date Kuta Software – Infinite Algebra 2 The Meaning Of Logarithms Rewrite each equation in exponential form. 1) log, 36 = 2 2) log 289 17= 4) log, 81 = 4 3) log 14 196 – -2 Rewrite each equation in logarithmic form. 5) 60-8 6) 122 = 144 Rewrite each equation in exponential form. 10) log u= 4 Rewrite each equation in exponential form. 15 9) log 10) log, u=4 20 11) log, r = y 12) log 2 v = u 13) log, v=-16 14) log, x=-8 Rewrite each equation in logarithmic form. 15) -14 =v 16) 8′ = a 18) 6′ = x 1(3) – 1 Page / 2 – a + 19) 9′ = x 20) 69 = 123 Evaluate each expression. 21) log 64 22) logo 216 23) log, 16 24) log: 243 23) log, 16 24) log 3 243 25) log, 125 26) log, 4 27) log 343 7 28) log, 16 29) log 4 30) logo 216 Page 2/2 – Q + Simplify cash expression. acer Simplify each expression. 31) 12l0512 144 32) slog, 17 33) xlog, 72 34) 9lo, 20 12 – Q +
The Correct Answer and Explanation is :
Here is the solution for each problem, followed by a 300-word explanation of the process:
Rewrite each equation in exponential form:
1) ( \log 6 36 = 2 ): ( 6^2 = 36 )
2) ( \log 17 289 = 2 ): ( 17^2 = 289 )
3) ( \log 14 196 = 2 ): ( 14^2 = 196 )
4) ( \log 3 81 = 4 ): ( 3^4 = 81 )
Rewrite each equation in logarithmic form:
5) ( 6^0 = 1 ): ( \log 6 1 = 0 )
6) ( 12^2 = 144 ): ( \log 12 144 = 2 )
Rewrite each equation in exponential form:
10) ( \log u = 4 ): ( 10^4 = u )
11) ( \log 20 r = y ): ( 20^y = r )
12) ( \log 2 v = u ): ( 2^u = v )
13) ( \log 3 v = -16 ): ( 3^{-16} = v )
14) ( \log 5 x = -8 ): ( 5^{-8} = x )
Rewrite each equation in logarithmic form:
15) ( -14 = v ): ( \log v (-14) = 1 )
16) ( 8^a = x ): ( \log 8 x = a )
18) ( 6^x = 3 ): ( \log 6 3 = x )
Evaluate each expression:
21) ( \log 2 64 ): ( 2^6 = 64 ), so ( \log 2 64 = 6 )
22) ( \log 6 216 ): ( 6^3 = 216 ), so ( \log 6 216 = 3 )
23) ( \log 2 16 ): ( 2^4 = 16 ), so ( \log 2 16 = 4 )
24) ( \log 3 243 ): ( 3^5 = 243 ), so ( \log 3 243 = 5 )
25) ( \log 5 125 ): ( 5^3 = 125 ), so ( \log 5 125 = 3 )
26) ( \log 2 4 ): ( 2^2 = 4 ), so ( \log 2 4 = 2 )
27) ( \log 7 343 ): ( 7^3 = 343 ), so ( \log 7 343 = 3 )
28) ( \log 4 16 ): ( 4^2 = 16 ), so ( \log 4 16 = 2 )
29) ( \log 6 36 ): ( 6^2 = 36 ), so ( \log 6 36 = 2 )
30) ( \log 6 216 ): ( 6^3 = 216 ), so ( \log 6 216 = 3 )
Simplify expressions:
31) ( \log 12 (12^2) ): Simplifies to ( 2 )
32) ( 5 \cdot \log 7 7 ): Simplifies to ( 5 \cdot 1 = 5 )
33) ( x \cdot \log 7 72 ): No simplification without more context.
34) ( 9 \cdot \log 5 20 ): No simplification without more context.
Explanation
Logarithms are the inverse operation of exponents. If ( b^e = a ), then ( \log b a = e ). This means the base ( b ) raised to the power ( e ) gives ( a ). Converting between logarithmic and exponential forms involves identifying the base, exponent, and result. For evaluation, find ( e ) that satisfies ( b^e = a ). Simplifications rely on logarithmic properties, such as ( \log b (b^k) = k ).