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?

Question

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?

yotaniwc · Accepted Answer

... and without logarithms or knowing any powers of 2 other than the most trivial one ...  24x+1=128    24x+1−1=24x=1282=64    24x−1=32    24x−2=16    24x−3=8    24x−4=4    24x−5=2    24x−6=1=20    so 4x−6=0 and x=64=32.

Nadine Salcido · Accepted Answer

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

Vasquez · Accepted Answer

24x+1=128 log⁡22x+1=log⁡128 (4x+1)×log⁡2=log⁡128 -from properties of logs x=14(log⁡128log⁡(2)−1)=32 note that you can use any logarithm, log base 10 or &#039;ln&#039; - or any other &#039;base&#039; 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