How to find the value of an unknown exponent? E.g. I have the question: 24x+1=128...

fertilizeki

fertilizeki

Answered

2021-12-31

How to find the value of an unknown exponent?
E.g. I have the question:
24x+1=128
I solved this by knowing that 128=27 and therefore x must equal 1.5.
However, is there a way of solving this without knowing that 128=27?

Answer & Explanation

yotaniwc

yotaniwc

Expert

2022-01-01Added 34 answers

... and without logarithms or knowing any powers of 2 other than the most trivial one ...
24x+1=128
24x+11=24x=1282=64
24x1=32
24x2=16
24x3=8
24x4=4
24x5=2
24x6=1=20
so 4x6=0 and x=64=32.
Nadine Salcido

Nadine Salcido

Expert

2022-01-02Added 34 answers

24x+1=128
log224x+1=log2128
4x+1=7
4x=6
x=64
Vasquez

Vasquez

Expert

2022-01-09Added 457 answers

24x+1=128
log22x+1=log128
(4x+1)×log2=log128 -from properties of logs
x=14(log128log(2)1)=32
note that you can use any logarithm, log base 10 or 'ln' - or any other 'base' of logarithms you might have (with log10 and loge being the commonly found ones on calculators, spreadsheets etc ) you have to use your chosen type of log consistently of course

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