Solve the exponential equations: a.) 4^-x = 64 b) 5^-x = 25 Solve the logarithm

Question

Solve the exponential equations: a.) 4^-x = 64 b) 5^-x = 25 Solve the logarithm equations: a.) log_3 (4x + 7) = 3 b.) log_7 (3x - 4) = 2 Calculate the value of the expression using properties of logs: a.) log_12 6 + log_12 2 = log_8 32 = b.) log_8 2 + Solve the equations using properties of logs; a) 3 log_11(x) = 2 log_11 8 = 3 log_5 9 b) 2 log_5(x) Solve the problems on compound interest: a.) How much will an investment of $100 become at 8% interest, compounded monthly over 5 years? b.)How long value if it is does it take an investment to double in value if it is invested at 6% compounded monthly?

Explanation / Answer

1) a) 4^-x = 4^3

x = -3

b) 5^-x = 5^2

x = -2

2) a) (4x+3) = 3^3

x = 6

b) 3x - 4 = 7^2

x = 53/3

3) a) log12(6*2) = log1212 = 1

b) log82*32 = log8 64 = 2log 88 = 2

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