Question

2^x+5 = 3^1-x use logarithms to solve the exponential equation. round answer to 3 decimal places.

Answer 1

$2^{x+5}=3^{1-x}\ \ \ \ \ /log_2()\\\\log_22^{x+5}=log_23^{1-x}\\\\x+5=(1-x)log_23\\\\x+5=log_23-xlog_23\\\\x+xlog_23=log_23-5\\\\x(1+log_23)=log_23-5\ \ \ \ /:(1+log_23)$

$x=\frac{log_23-5}{1+log_23}\\-------------\\log_23\approx1.5849625\\----------------\\x\approx\frac{1.5849625-5}{1+1.5849625}\approx-1.321$

Answer 2

2^x+5 = 3^1-x
take log on both sides
(x+5)log2=(1-x)log3
0.3010(x+5) = (1-x)0.4771
0.3010x + 1.5050 = 0.4771 - 0.4771x
0.7781x= -1.0279
x=-1.320