I am given the expression $3^{4x-5}=38$ and asked to rewrite in common log to isolate the variable $x$, then to solve using a calculator.
I am struggling to to get the $x$ on it's own. My attempt:
$$3^{4x-5}=38$$
Rewrite lhs as a log
$$log_3(4x-5)=38$$
Rewrite lhs into common log base 10:
$$\frac{log(4x-5)}{log(3)}=38$$
This is as far as I can go. How can I isolate x here?
[Edit]
I rewrote to this, does it look right?
$$3^{4x-5}=38$$
$$log_3(38)=4x-4$$
My textbook says I am specifically to rewrite using the common log:
$$\frac{log(38)}{log(3)}+5=4x$$
$$x=\frac{(\frac{log(38)}{log(3)}+5))}{4}$$
Best Answer
Hint: $\log a^b = b \log a$ and not $\log_ba$