For a real number x, if $$\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$$, and $$\frac{\log_5\left(2^x + \frac

Question

For a real number x, if $$\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$$, and $$\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$$ are in an arithmetic progression, then the common difference is

Accepted Answer

log ⁡ 4 ( 7 2 ) \log_4\left(\frac{7}{2}\right) lo g 4 ​ ( 2 7 ​ ). It is given that 1 2 , log ⁡ 3 ( 2 x − 9 ) log ⁡ 3 4 \frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4} 2 1 ​ , l o g 3 ​ 4 l o g 3 ​ ( 2 x − 9 ) ​ , and log ⁡ 5 ( 2 x + 17 2 ) log ⁡ 5 4 \frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4} l o g 5 ​ 4 l o g 5 ​ ( 2 x + 2 17 ​ ) ​ are in an arithmetic p

For a real number x, if $\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$ , and $\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$ are in an arithmetic progression, then the common difference is

For a real number x, if $\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$ , and $\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$ are in an arithmetic progression, then the common difference is