How do you solve $2^{5 n - 5} + 2 = 75$ $2^(5n-5)+2=75$ ?

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Answer 1 · 2016-09-12T23:32:54

$2^{5 n - 5} = 73$ $2^(5n - 5) = 73$

$log (2^{5 n - 5}) = log 73$ $log(2^(5n - 5)) = log73$

$(5 n - 5) log 2 = log 73$ $(5n - 5)log2 = log73$

$5 n log 2 - 5 log 2 = log 73$ $5nlog2 - 5log2 = log73$

$5 n log 2 = log 73 + log 32$ $5nlog2 = log73 + log32$

$n = \frac{log 2336}{log 32}$ $n= log2336/log32$

The decimal approximation will be $n ≅ 2.24$ $n ~=2.24$ .

Hopefully this helps!

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