JAMB 1994 · UME · Q20

Find the value of $r$ if $\log_{10} r + \log_{10} r^2 + \log_{10} r^4 + \log_{10} r^8 + \log_{10} r^{16} + \log_{10} r^{32} = 63$ .

Worked solution (try it first)

Bring each power down: the left side is $(1 + 2 + 4 + 8 + 16 + 32)\log_{10} r = 63\log_{10} r$ .
So $63\log_{10} r = 63$ , and $\log_{10} r = 1$ .
Change to index form: $r = 10^1 = 10$ , option C.