maths please help and explain

1.evaluate without using a calculator

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

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  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

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