How do you solve $7^(2x-3) - 4 = 14$ ?

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Answer 1 · 2016-04-06T03:50:49

You must work with the fact that $a^n = m -> loga^n = logm$

$7^(2x - 3) = 18$

$log7^(2x - 3) = log18$

Simplify using the rule $loga^n = nloga$

$(2x - 3)log7 = log18$

$2xlog7 - 3log7 = log18$

$2xlog7 = log18 + 3log7$

Use the rule $log_an + log_am = log_a(n xx m)$

$x(2log7) = log(18 xx 343)$

$x = log6174/log49$

$x = 2.24$

Make sure to ask your teacher whether or not they require your answer in logarithmic (exact) form.

Hopefully this helps!

How do you solve 7^(2x-3) - 4 = 147^(2x-3) - 4 = 14?