1.evaluate without using a calculator

Question

2logx+1=log900

2.solve the following equation

A. 3log(x-2)=4.714
B. 16^x-3 = 8^2x+1
C.10^2x=1/100

Answer 1

2logx + 1 = log900
since 1 = log10,
2logx + log10 = log900
log x^2 + log10 = log900
log(10x^2) = log 900
10x^2 = 900
x^2 = 90
x = √90

3log(x-2) = 4.714
log(x-2)^3 = 4.714
(x-2)^3 = 51760.68
x-2 = 37.268
x = 39.268

16^(x-3) = 8^(2x+1)
since 16 = 2^4 and 8 = 2^3,
2^(4(x-3)) = 2^(3(2x+1))
4x-12 = 6x+3
2x = -15
x = -15/2

10^2x = 1/100
10^2x = 10^-2
2x = -2
x = -1